Analysis Parameters
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\r\n\tQuantum mechanics arose in 1924 and was developed by scientists such as Einstein, Bohr, Schrodinger, Heisenberg, Born, Dirac, and many others.
\r\n\t
\r\n\tQuantum mechanics has subsequently been applied to many of the phenomenon physicist studies, such as atoms, molecules, nuclei, and even neutron stars, superfluids, and elementary particles. It is hoped this book will be able to examine both the mathematical and conceptual aspects of quantum physics by presenting papers that discuss both its mathematical basis and philosophical interpretation. It is hoped this new collection of papers will stimulate the study and expansion of this area of modern physics.
The adaptive noise cancellation has proved being very efficient method in various practical applications such as voice clearance, recognition systems for voice, hands-free telephony, and medical applications such as hearing aids and fetal electrocardiography [1], etc. Figure 1 [1], depicts the basic principle of noise cancellation (understanding that noise is an unwanted signal, d(n)), which is described by main signals that feed the system.
\n\t\t\tAdaptive noise cancelling approach
Acoustic noise has been studied in recent years due to growing interest in cancelling acoustic noise through active control, since it is increasingly common to find sources of noise in many industrial processes. Basic outlines of noise cancellation were based on the application of passive attenuators that were used for many years without much success [2], however, development of digital signal processing has become increasingly feasible systems active noise cancellation. Active noise cancellation systems cancel unwanted acoustic noise based on the superposition principle: an acoustic noise of equal amplitude but opposite phase is generated in order to cancel out the unwanted noise.
\n\t\t\tThis work discusses a scheme of active noise cancellation using adaptive algorithms of the digital filters required for the correct operation of the proposed system. The signal generation "anti-noise" to cancel the primary source of noise is a problem different from change of environment, since the signal is generated by electrical means and must be propagated acoustically to have the desired effect; this creates a delayed signal in the generation and propagation, so this change is necessary to calculate the required signal. This work considers the estimation of this modification done "offline" [2].
\n\t\t\tHybrid ANC systems correspond to a combination of control structures from the feedback and feedforward systems, where the cancelling signal is generated based on the outputs of both the reference sensor and the error sensor. While the feedforward system attenuates the primary noise, which is correlated with the reference signal, the feedback system cancels the predictable components of the primary noise signal that are not observed by the reference sensor.
\n\t\t\tAs an example of the efficiency of the adaptive hybrid systems, this work evaluates a Hybrid Active Noise Control (HANC) system under feedback acoustic situation. Proposed scheme objective is to compare the performance of HANC versus common references: feedback, feedforward and neutralization systems; the inner nature of HANC gives two main characteristics: on line modeling of secondary path and a good performance under acoustic feedback conditions. In the evaluated system, two least mean square (LMS) adaptive filters are used in the noise control process: one for the feedforward stage and the other for the feedback stage; both of them use the same error signal as used in the adaptation of the modeling filter. Then, the combination of the feedback and feedforward stages, results in a solid robustness for the system in acoustic feedback situation.
\n\t\t\tThis chapter discusses a vital application in telecommunications processes, which is the echo in telephone line and the same time a new proposal: the hybrid structure proposed as a solution to this problem. Finally, the computer simulations are presented to show the success of the proposed system. So, this chapter presents an adaptive hybrid system to resolve the problems described: the noise cancellation using adaptive filtering and one proposal for echo cancellation system. Furthermore, we present a hybrid structure which consists of a feedforward structure, used to estimate the noise path, and a feedback structure, used to cancel the noise, i.e., the unwanted signal: echo in telephony systems or noise signals like conversations, snoring or engines. Hybrid active noise cancellation systems are a good solution to these two important problems, since they have the properties of both the feedforward and feedback systems.
\n\t\tAn adaptive filter responds to changes in its parameters like its resonance frequency, input signal or transfer function that varies with time, for example. This behavior is possible since the adaptive filter coefficients vary over time and are updated automatically by an adaptive algorithm. Therefore, these filters can be used in applications where the input signal is unknown or not necessarily stationary. An adaptive filter is composed of two parts: digital filter and adaptive algorithm.
\n\t\t\t\tOne of the most important applications for this kind of system is active noise control (ANC). ANC systems must respond to changes in frequency of the primary noise they want to cancel out. In other words the primary non-stationary noise varies; hence we must use some kind of adaptive system, to get an acceptable cancellation that carried out many operations at a high speed. The ability of an adaptive filter to operate and respond satisfactorily to an unknown environment, and variations that may be involved in signal reference, to make a powerful adaptive filter for signal processing and control applications. There are several types of adaptive filters but generally all share the characteristic of working with an input signal (input vector), and a desired response (output vector). These two signals are used to compute an estimate of error (error signal), which allows control of the coefficients of the adjustable filter.\n\t\t\t\t
\n\t\t\t\tIn other words, ANC is an approach to noise reduction and a secondary noise source that destructively interferes with the unwanted noise is introduced. In general, active noise control systems rely on multiple sensors to measure the unwanted noise field and the effect of the cancellation. The noise field is modeled as a stochastic process, and an adaptive algorithm is used to adaptively estimate the parameters of the process. Thus, active noise control involves an electroacoustic or electromechanical system that cancels the primary (unwanted) noise based on the principle of superposition; specifically, an anti-noise of equal amplitude and opposite phase is generated and combined with the primary noise, thus resulting in the cancellation of both noises. ANC is developing rapidly because it permits improvements in noise control, often with potential benefits in size, weight, volume, and cost. Thus, the active noise control has been object of an intense research and central subject in many scientific articles in the last 10 years.
\n\t\t\t\tOn the other hand, unwanted acoustic noise is a by-product of many industrial processes and systems. This problem has become more and more evident as the applications of electronic communication systems increase, since their effects represent an important source of annoyances for the end user and they can reduce considerable the efficiency, the quality and the reliability of this type of systems. These ANC systems use an active form of noise control which includes the use of a second source of sound that generates a signal of the same characteristic as echo but with different phase. This allows to cancel this signal because the waves of sounds propagate linearly, which is known as superposition effect Also, since the characteristics of the signal to cancel change constantly, in this case the echo, the system requires a great capacity of adaptation. These adaptively systems, represent a feasible alternative for echo cancellation in telephone lines due to their processing, capacity and lower cost.
\n\t\t\tTelephone echo, is a phenomenon produced by the mismatching impedance of the hybrid circuit used to couple the two lines with the four lines sections of long distance communication systems that considerably degrades the quality of telecommunication systems. Several systems have been proposed in the literature during the last several years, to solve these problems, such as adaptive echo cancelers. The figure 2 depicts the basic structure of described system.
\n\t\t\t\tEchocancelling in long distance telephone systems
An echo canceler generates a replica of the echo signal and subtracts it from the signal to be transmitted generating the so-called pseudo echo, which is then used to update the echo canceler coefficients such that the mean square value of residual echo becomes a minimum. However the real time estimation of the hybrid impulse response is a difficult task for several reasons:
\n\t\t\t\tThe echo path impulse response is non-stationary, and then the convergence of adaptation algorithm must be fast enough to track these changes.
The power spectral density of speech signals is not flat. This fact results in a slower convergence rate when gradient search based adaptive algorithms are used.
In most cases the echo canceler requires one hundred or more taps for an accurate estimation of a hybrid impulse response and several thousand of taps in the acoustic echo path case, which makes the use of efficient adaptation algorithms difficult.
The presence of both, near and far-end speakers simultaneously often occurs, which require some robust mechanisms or adaptation algorithms to handle it. Thus the development of low complexity and high convergence rate echo canceler structures has received a lot of attention, resulting in several efficient echo canceler structures and adaptation algorithms.
The most suitable tool for solving the two aforementioned problems is adaptive filtering which has been successfully applied in the solution of several practical problems [3].
\n\t\t\t\n\t\t\t\t\t\tFigure 4 shows, in a simplified way, an ANC Feedforward System, in which the digital filter W(z) is used to estimate the unknown plant P(z). It is assumed that both the plant and the filter have the same input signal x(n). Moreover, a Filtered LMS (Filtered-X Least Mean Square, FXLMS) algorithm is introduced, which is a varying form of the LMS algorithm [2]. FXLMS algorithm solves the secondary path problem, described as the set of transformations that the filter signal and the adaptive error signal go through, on their way from an electric to an acoustic domain. During this electro-acoustic process, the signal may be delayed or altered in such a way that it is necessary to minimize such effects. The FXLMS algorithm technique consists of placing a filter, with the same properties as the secondary path, in the reference signal going towards the adaptive least mean square filter (LMS), as shown in figure 3.
\n\t\t\t\t\tANC Feedforward system with FXLMS algorithm
From Figure 3, filter Ŝ(z) is the model of the secondary path, defined by filter S(z). Taking this into consideration, the update of filter W(z) is given as follows:
\n\t\t\t\t\tWhere
\n\t\t\t\t\tThere are some situations in which it is not possible to take into account the reference signal from the primary noise source in a Feedforward ANC system, due to difficult access to the source, or another reason that makes it hard to identify a specific signal through the reference microphone. A solution to this problem is to introduce a system, which will predict the behavior of the input signal; this system is known as a posteriori ANC (Feedback ANC), which is known for using only an error sensor and a secondary sound source to achieve noise control.
\n\t\t\t\t\t\n\t\t\t\t\t\tFigure 4 describes a Feedback ANC system with FXLMS algorithm, in which d(n) is the noise signal, e(n) is the error signal, defined as the difference between d(n) and signal y’(n), which is the adaptive filter’s output once the secondary path has been crossed. Finally, the adaptive filter’s input signal is generated by the sum of the error signal and the resulting signal from the convolution between the secondary path Ŝ(z) and the estimated output of the adaptive filter, y(n).
\n\t\t\t\tFeedback ANC system with FXLMS algorithm
A hybrid ANC system is made up of an identification stage (feedforward) and a prediction stage (feedback). The combination of both stages needs two reference sensors: one close to the primary noise source and other with the residual error signal. Figure 6 shows the detailed block diagram of a hybrid ANC system, in which it is possible to observe the basic systems (Feedforward, Feedback) involved in the design. The attenuation signal, given by y(n), results from the addition of both adaptive filter outputs, W(z) and M(z). Filter M(z) represents the Feedback process of the adaptive filter, while filter W(z)represents the Feedforward process. The secondary path in the basic ANC system is also taken into consideration in the hybrid system, and is given by the transfer function S(z).
\n\t\t\t\tAmong the advantages of hybrid ANC systems we can mention:
\n\t\t\t\tThe fact that lower order filters may be used to achieve the same performance;
The other two systems present much more significant plant noise than the hybrid system;
The combination of both systems allows for much more flexibility in regards of design; and,
Cancellation of both narrowband and broadband noise.
Hybrid ANC system with FXLMS Algorithm
The block diagram if the hybrid ANC system in Figure 5 also shows FXLMS algorithm to make up for the possible delays or problems induced by the secondary path [4].
\n\t\t\tAs mentioned previously, the process that transforms the resulting signal from the adaptive filter y(n) into signal e(n), is defined as secondary path. This characteristic takes into consideration the digital to analog converter, the reconstruction filter, the sound source, the amplifier, the acoustic path from the sound source to the error sensor, the error microphone, and the analog to digital converter. There are two techniques to estimate the secondary path, both with characteristics that make each method more comprehensive and sophisticated in certain ways; these techniques are: offline secondary path modeling and online secondary path modeling. The first method is performed with a Feedforward system, where the plant is now S(z) and the coefficients from the adaptive filter are the secondary path estimation, as shown in Figure 6 [4].
\n\t\t\t\tOffline Secondary Path Modeling
This property is typical of feedforward systems. Figure 7 shows the contribution of attenuation signal y(n), which causes the system to degrade because of the signal present in the reference microphone.
\n\t\t\t\t\t\n\t\t\t\t\t\t\t\tFeedforward ANC process with acoustic feedback
Two possible solutions for acoustic feedback problem are: acoustic feedback neutralization and the proposal of a hybrid system, which has a better performance in the frequency range and attenuation level of interest [4]. To evaluate this approach, we used a hybrid system as shown in Figure 8, where F(z) is the transfer function of the feedback process.
\n\t\t\t\t\t\n\t\t\t\t\tThe system proposed in [5] will be analyzed and this system, with a set of signals and experimental conditions, was completely evaluated in [6].
\n\t\t\t\tMost common way to eliminate acoustic feedback is to make an online path modeling, like indicated on [3] and, more recently, in relevant papers by [7] and [8]. However, one of the main characteristics of the hybrid system presented by the authors in [9] is that it does not take the secondary path modeling into consideration. Instead, the proposed hybrid system takes advantage of the inherent robustness of hybrid systems when it comes to acoustic feedback, figure 8.
\n\t\t\t\t\tHybrid ANC system with acoustic feedback
The system in Figure 9, proposed by [10], was used to compare the robustness of the HANC system against the neutralization system.
\n\t\t\t\t\tKuo’s Neutralization System
The details of the system in Figure 9 can be consulted in [10]. However, an important fact of this system is that it uses additive noise for modeling, also, as mentioned in [7], regarding predictable noise sources.
\n\t\t\t\tThe echo is a problem that significantly degrades the quality of telecommunication systems. This occurs, in telephone line, due to the decoupling impedance hybrid which exists in the coils and are used to couple subscriber communication channel with the long distance channels. There is also the so-called acoustic echo which occurs in teleconferencing systems and hands free telephone systems. This type echo occurs due to acoustic coupling between loudspeakers and microphones used in these communication systems.
\n\t\t\t\tSeveral systems which try to solve this problem have appeared in the literature in recent years. Among these are: directional microphone arrangement [11], echo suppressors and adaptive echo cancellers [11, 12], etc. Among them, adaptive echo cancellation seems to be the best way to reduce the echo problem [13, 14]. An echo canceller generates an echo replica and subtracts the signal to be transmitted, generating a so-called residual echo. The echo residual is then used to adapt the coefficients of the system, using in most cases a gradient-based algorithm, in a way that the mean square value of the residual echo is progressively minimized [11, 12, 13, 14]. However, the real-time estimate of the impulse response of the hybrid or echo channel is a complex problem for several reasons:
\n\t\t\t\t1. The duration of the impulse response of a typical echo channels in teleconferencing systems in the order of several hundreds of milliseconds, which means that transversal filter coefficients of several thousand would be needed to reduce echo to acceptable levels. The impulse response of a typical acoustic echo channel is shown in Figure 10.
\n\t\t\t\t2. The impulse response of echo channel is non-stationary because it changes with the movement of the interlocutors, or the number of active subscribers on a given time. Thus the adaptive algorithm should be fast enough to track those changes.
\n\t\t\t\t3. The power density spectrum of the voice is not flat, and in many cases reduces speed of convergence of the adaptive algorithm. The correct estimate of the echo channel using structures with the least possible complexity and the relatively high speeds obtain convergence of the adaptation algorithm, as mentioned above, are non-trivial problems which have received considerable attention in recent years; among the different proposed have been proposed several echo cancellation systems, among we can mention: transverse echo cancellers, echo cancellers in the frequency domain, echo cancellers infinite impulse response subband echo cancellers, etc., [11, 12, 13, 14].
\n\t\t\t\t\n\t\t\t\tBesides the reduction in the complexity of the canceller, to allow correct estimation of the echo channel and the development of adaptive algorithms with rapid convergence, another major problem is handle the simultaneous presence of echo near the speaker\'s voice. The situation we want to avoid is to interpret the speaker\'s voice echoing nearby, and make great changes in the echo channel estimated in an unsuccessful attempt to cancel this. A checked algorithm could operate incorrectly when the distant partner is present, so it is necessary to incorporate certain mechanisms within the system to avoid this effect [11, 12, 13, 14].
\n\t\t\t\tA typical impulse response of acoustic echo channel
There are few references about the convenience of using adaptive hybrid schemes for solving the problem of echo cancellation, and given the results obtained for applications for cancellation of acoustic noise [15], hybrid scheme is proposed for electrical noise cancellation, since it is on the phone lines where there is the problem described. Be detailed later about how to do and the results achieved.
\n\t\t\tA long distance telephone system basically consists of a 2-wire portion, known as the subscriber circuit, and connects the subscriber to the local exchange and long-distance circuits itself; this system consists of a transmission channel and another receiving, each of which consists of two wires. A hybrid transformer is used to couple circuits’ long distance subscriber circuit and ideally isolate the transmission channels and reception of long-distance circuit. However due to the decoupling impedance, they are not completely isolated so that a portion of the received signal is delayed in the form of echoes. A similar problem arises in teleconferencing systems with so-called acoustic echo which occurs due to coupling between the microphone and speaker in the teleconference system. This result in a delayed and distorted replica of the signal produced by the loudspeaker is fed back into the microphone.
\n\t\t\t\tIn both cases there is deterioration in the communication system, which resulted in the appearance of echo cancellers. These cancellers have proved to be the best way to solve this problem [11, 12]. The basic principle of echo cancellation, which is illustrated in Figure 11, is to generate an echo replica, this is subtracted from the signal to be transmitted, resulting in the so-called residual echo that consists of part of the signal echo which could not be canceled more near the speaker\'s voice, if this is present [11, 12]. The residual echo is then used to adapt the parameters of the canceller in such a way that the residual echo power is progressively minimized.
\n\t\t\t\tEchocancelling in long distance telephone systems
Echo canceller consists of two main parts. An adaptive filter, which generates an echo replica and is subtracted from the signal being transmitted, and a system commonly known as double-talk detector, this system prevents distortion due to the presence of the speaker\'s voice service or in the absence of the partner away. The first component is the structure of the adaptive filter along with its adaptation algorithm.
\n\t\t\t\tSome researchers have resulted in the appearance of various structures, such as transversal filters, subband structures, structures in the frequency domain, etc., and various adaptive algorithms, mostly based on gradient descent search. Second component, despite its importance, has received much less attention than the first component. Thus conducting research aimed at developing highly reliable mechanisms to avoid distortion due to the simultaneous presence of both parties, "double-talk detector," especially when using algorithms based on gradient descent search is of great importance.
\n\t\t\t\n\t\t\t\t\tFigure 12 shows the block diagram of the evaluated hybrid ANC structure with online secondary path modeling. This hybrid ANC structure consists of a feedforward stage, W(z), which is used to estimate the noise path, P(z), and a predictive structure, M(z), which is used to cancel the distortion due to the acoustic feedback path, F(z). Since the samples of feedback distortion are strongly correlated among them, they can be predicted [15].
\n\t\t\t\tAs shown in Figure 12 signal, a(n), is used simultaneously as:
\n\t\t\t\tThe error signal to update the adaptive filter, W(z), which corresponds to the feedforward stage used to identify the noise path, and,
To update the linear predictive filter M(z), which intends to cancel the distortion produced by the feedback propagation from the canceling loudspeaker to the input microphone thorough the system F(z); and,
To estimate
Evaluated hybrid ANC structure
The hybrid ANC contains the advantages of feedback and feedforward systems. The model presented by [16] was modified to adapt the system for a specific objective: reduce the residual echo. This system uses two input signal x(n) and din(n), one for each talker. The plant that models echo refers to the effect of mismatch of impedance present in the telephone circuit. The echo signal is d(n) and the residual echo plus the far-end signal is represented by e(n). This system incorporates the signal of the feedforward and the feedback effect that means both systems contribute to generate the cancelling signal, which approximates to the echo signal. Also this system includes a switch on the feedback system: when the echo signal and the far-end signal are highly correlated, the feedback system cancels part of the far-end signal even if the hybrid system already converged [17].
\n\t\t\t\tAdapted Hybrid ANC for Active Echo Cancellation
To analyze the system is necessary to consider the correlation between signals, as shown in the equation (3):
\n\t\t\t\tThe cross correlation vector between the entrance and the echo is given by:
\n\t\t\t\tand the correlation matrix can be written as follows:
\n\t\t\t\twhere \n\t\t\t\t\t\t
There are two kinds of echo: electric and acoustic. The electric echo is present in traditional telephony lines because of the impedance mismatch of the conversion (from two to four wires). The acoustic echo is the direct or indirect feedback of reflected signals to the microphone during a conversation. There are two controls applied to echo: suppressor and canceller systems. Echo Cancellation systems need to consider the disturbances in the far-end talker\'s signal and the superposition of the near-end talker\'s that generates double-talk. Two general approaches are the use of suppressors and the use of cancellers. The echo suppressor has a sensor that measures the voice signal power in each part of the circuit to decrease the impact of the echo. The echo suppressor changes the full duplex channel to a half-duplex channel [14, 18]. This characteristic is a disadvantage of this type of control because it cancels part of the speech. Echo cancellers use the superposition principle that means this system generates a similar signal with delay and attenuation similar to the transmitted signal. It is recommended to train the system to approach the characteristics of the echo signal. For this problem some authors [19, 20], offered different solutions based on Double-Talk Detector (DTD) [21]; this principle detects the presence of simultaneous speech of both talkers and pause the coefficient updating of the adaptive filter. It is known that the adaptive filter is the key to treat echo problems. It is necessary to consider the speed of convergence and robustness of the system. Most of echo cancellation systems use transversal filters and the LMS algorithm or variations of this to adjust the coefficients [22].
\n\t\t\t\tThe result is an error signal named as residual echo signal due to estimation of the adaptive filter [21], this scenario, adapted to an ANC system is shown in Figure 14 [3].
\n\t\t\t\tSystem identification viewpoint of ANC
From Figure 14, the residual echo e(n) is defined as
\n\t\t\t\twhere d(n) is the echo signal and y(n) is the response generated by the adaptive filter after processing the algorithm. Also [3], presents the criteria of the Mean Square Error (MSE) to find the convergence point of the system. To analyze the performance of the Echo Cancellation system Echo Return Loss Enhancement (ERLE) criteria was developed. The ERLE criterion is described in equation (8).
\n\t\t\t\tERLE parameter was used to evaluate the present proposed system.
\n\t\t\tThe proposed system has different parameters to consider. These parameters determine whether the system converges or not.
\n\t\t\t\t\n\t\t\t\t\t\t\tStep size (μ): controls the system stability and speed of convergence, one for each part of the system (feedback and feedforward).
Plant: simulates the echo effect
Adaptive filter\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\tNumber of blocks and iterations: reflected in the number of samples observed
Entrance signals: including the near-end and the far-end
Step size values were taken by [16, 23]. The plant simulates the effect of echo that the near-end suffer because of the impedance mismatch, proposed by [24].
\n\t\t\t\tThe input signals utilized are sorted into one of three types, considering the classification proposed by [3, 25], as well as companies such as [26].
\n\t\t\t\t\n\t\t\t\t\t\t\tContinuous; the level of sound remains constant or nearly constant with small fluctuations. For Echo cancellation, the selected signals were vacuum, four tones and silence.
\n\t\t\t\t\t\t\tIntermittent: the level of sound presents some fluctuations that can be periodic or random. The selected signals are real voices recorded in a computer for Echo considerations.
\n\t\t\t\t\t\t\tImpulsive: the level of noise presents impulses in a brief period of time.
For Acoustic Noise Reduction applications, the system was tested with several real sound signals taken from an Internet database [27]. The sound files were selected taking into account that the system is to be implemented in a duct-like environment. Also, six different types of signals were used for the analyzed system:
\n\t\t\t\tA sinusoidal reference signal with frequency of 300 Hz, and 30 dB SNR;
A reference signal composed of the sum of narrow band sinusoidal signals of 100, 200, 400, and 600 Hz; and,
The rest of the reference signals are.wav audio files with recordings of real noise sources, which are “motor” and “airplane”, as in [16].
The most important values are modeling error, as was defined by [28], and MSE, given by the ratio between the power of the error signal, and the power of the reference signal:
\n\t\t\t\tFor experience, we need to train the system before to start to work [16]. So, we have two considerations:
\n\t\t\t\tFor echo cancellation, we adapt the plant for 20 representative coefficients instead the 1000 given by [24]. The adaptive filter was a vector of 20 coefficients initialized in zero. The near-end voice was a female voice and silence for the far-end. The step size value were change until get the higher level of ERLE, after run the simulation of the system using Matlab®, with a software interface developed specifically for this purpose, the results of the adaptive filter were retaken to repeat the processing, when a 40dB of cancellation were achieve the training was stopped. The scenario for training work was single-talk with a single voice signal in the near-end.
For the situation for Acoustic Noise Reduction, secondary path is offline modeling stopped when the error is reduced-35dB similar to [15]. The excitation signal v(n) used was white Gaussian noise with variance of 0.05.
To consider an approximation of a real system the results of processing echo of voice with the hybrid proposed system. We present the results using the female voice signal (Figure 15) in the near-end and two different masculine voice signals in far-end (Figure 16 and Figure 17).
\n\t\t\t\tFemale voice signal
First masculine voice signal
Second masculine voice signal
The echo signal generated by the adaptation of the plant is represented in the Fig 18.
\n\t\t\t\tEcho of the female voice signal with adapted plant
Applying the function with the parameters of Table 1, the obtained results are shown in Figure 19 and Figure 20. Both figures show that system achieves cancellation of the echo signal.
\n\t\t\t\tParameters | \n\t\t\t\t\t\t\tValue | \n\t\t\t\t\t\t
Step size | \n\t\t\t\t\t\t\t0.1 | \n\t\t\t\t\t\t
Plant | \n\t\t\t\t\t\t\tFrom [24] | \n\t\t\t\t\t\t
Blocks | \n\t\t\t\t\t\t\t1000 | \n\t\t\t\t\t\t
Iteration | \n\t\t\t\t\t\t\t80 | \n\t\t\t\t\t\t
Analysis Parameters
ERLE using female voice in the near-end and masculine voice 1 in far-end
ERLE using female voice in the near-end and masculine voice 2 in far-end
Cancelling voice signal, system with masculine voice 1
Cancelling voice signal, system with masculine voice 2
Looking for a detailed analysis in the cancelling signal (Figure 21), which imitates echo signal, for the first masculine signal, the system begins to diverge. This occurs because of the high correlation between the two entrances voices; this effect is given by the feedback because even when the system already converge starts to cancel the far-end signal [29].
\n\t\t\t\t\n\t\t\t\tThen, instead of the first male signal, another signal was used and the system converged better, this can be seen in Figure 22, this situation is because the correlation between this signal and the female is smaller.
\n\t\t\t\t\n\t\t\t\tAs mentioned before, the step size factor has a major impact on the development of the system, and proved to be the main reason to make the system converge; additional simulations were performed using the parameters in Table 2; this means a smaller size step and the male voice first.
\n\t\t\t\tParameters | \n\t\t\t\t\t\t\tValue | \n\t\t\t\t\t\t
Step size | \n\t\t\t\t\t\t\t0.01 | \n\t\t\t\t\t\t
Plant | \n\t\t\t\t\t\t\tFrom [24] | \n\t\t\t\t\t\t
Blocks | \n\t\t\t\t\t\t\t1000 | \n\t\t\t\t\t\t
Iteration | \n\t\t\t\t\t\t\t80 | \n\t\t\t\t\t\t
Analysis Parameters for Additional Test
The system improves its performance using the parameters of Table 2. The generated cancelling signal (Figure 23), does not have impulsive periods.
\n\t\t\tCancelling voice signal, system with masculine voice 1 and adjusted step size
This section presents the simulation experiments performed for acoustic noise reduction. First, an offline modeling was used to obtain FIR representations of tap weight length 20 for \n\t\t\t\t\t\t\t
Various articles on the subject of ANC were references taken into consideration before establishing main analysis parameters to determine the hybrid system’s performance:
\n\t\t\t\t\ta) Filter order; it is important to evaluate the system under filters of different orders. In this case, 20 coefficients were selected (we considered the fact that the distance between the noise source and the control system is not supposed to be very large).
\n\t\t\t\t\tb) Nature of the filter coefficients; on a first stage, the coefficients were set according to real values taken from a previous study made on a specific air duct [2]. These coefficients were taken from the work done in [16] to determine the values of the primary and secondary path filters for an air duct.
\n\t\t\t\t\tThe simulation results are presented according to the following parameters:
\n\t\t\t\t\tMean Square Error (MSE); and
Modeling error from online secondary path modeling.
\n\t\t\t\t\t\tTable 3 shows the values used for the feedforward and feedback step sizes, as well as the range of step sizes used for the secondary path filter. The values were set by trial and error, starting with the values that were determined with the previous test.
\n\t\t\t\t\tSignal | \n\t\t\t\t\t\t\t\tStep size μw, μm\n\t\t\t\t\t\t\t\t | \n\t\t\t\t\t\t\t\tStep size μs\n\t\t\t\t\t\t\t\t | \n\t\t\t\t\t\t\t
Continuous | \n\t\t\t\t\t\t\t\t0.000001 | \n\t\t\t\t\t\t\t\t0.0001 – 0.001 | \n\t\t\t\t\t\t\t
Intermittent | \n\t\t\t\t\t\t\t\t0.000001 | \n\t\t\t\t\t\t\t\t0.0001 – 0.001 | \n\t\t\t\t\t\t\t
Impulsive | \n\t\t\t\t\t\t\t\t0.000001 | \n\t\t\t\t\t\t\t\t0.0001 – 0.001 | \n\t\t\t\t\t\t\t
Filters Step Size Used in Proposed Analysis
Also, a white noise with zero mean and variance equal to 0.05 was used in the system. Since there were not enough resources to implement an abrupt secondary path change (which means there was only one set of values available for the secondary path filter from [15], a gradual change was made, given by the sum of a sinusoidal function to the secondary path coefficients, from iteration 1000 to 1100. The best response was shown by the continuous signal; Figure 24 shows the Modeling error for this case, while Figure 25 shows the MSE.
\n\t\t\t\t\tRelative modeling error for continuous signal
MSE for continuous signal
From Table 3, it can be noticed that the step sizes had to be considerably reduced, in the order of 1000, in comparison to the values established for the tests with Echo cancellation. This is due to the fact that the coefficient values are not necessarily within a range of -1 to 1, so the secondary path modeling needs a smaller step size to be able to achieve convergence.
\n\t\t\t\t\tFor the intermittent signal, the effects of the small step sizes were similar: the system took more time to converge and the level of noise cancellation was reduced. Nonetheless, the response achieved stability during the simulation. Figure 26 and Figure 27 correspond to the Modeling error and MSE for the intermittent signal, respectively.
\n\t\t\t\t\tRelative modelling error for intermittent signal
MSE for intermittent signal
Finally, for impulsive input signal the results were not as good as expected. The results can be explained since there are very abrupt changes in the signal amplitude, and the step size is very small. Hence, the values of the coefficients tend to infinity and the simulation stops abruptly.
\n\t\t\t\tIn this section, three paths were used: the main or primary path P(s), the secondary path S(s), and the acoustic feedback path F(s). All the filters used in the evaluated proposals are finite response filters (FIR). The values of these paths are based on [2], and represent the experimental values of a given duct. A total of 25 coefficients will be used in all paths so as to report an extreme condition for a real duct under analysis.
\n\t\t\t\t\tTo initialize Ŝ(z), the offline secondary path modeling is stopped when the modeling error has been reduced up to -35dB, similar to [15]. The excitation signal v(n), is white Gaussian noise with variance equal to 0.05.
\n\t\t\t\t\tThe values for the step size are adjusted by trial-and-error to achieve a faster convergence and stability, following the guidelines from previous work on Hybrid Active Noise Control [16], and the values selected in [7] for neutralization. A summary of the selected values for μ, is shown in Table 4.
\n\t\t\t\t\tSystem | \n\t\t\t\t\t\t\t\tPrimary Path μP\n\t\t\t\t\t\t\t\t | \n\t\t\t\t\t\t\t\tSecondary Path μS\n\t\t\t\t\t\t\t\t | \n\t\t\t\t\t\t\t\tFeedback Path μF\n\t\t\t\t\t\t\t\t | \n\t\t\t\t\t\t\t
Neutralization System | \n\t\t\t\t\t\t\t\t0.000001 | \n\t\t\t\t\t\t\t\t0.00005 | \n\t\t\t\t\t\t\t\t0.00005 | \n\t\t\t\t\t\t\t
Hybrid System | \n\t\t\t\t\t\t\t\t0.001 | \n\t\t\t\t\t\t\t\t0.001 | \n\t\t\t\t\t\t\t\tNA | \n\t\t\t\t\t\t\t
Filters Step Size Used in Proposed Analysis
MSE with “sinusoidal” reference signal for Feedforward System
\n\t\t\t\t\t\tFigure 28 to Figure 41 show the result of the systems analysis with the previously mentioned set of signals. All results are shown in dBs, measuring the error power at the output (Mean Square Error).
\n\t\t\t\t\tFirst, we show the main signal for ANC systems, the sinusoidal signal. Figures 28 to 30 show the MSE value obtained.
\n\t\t\t\t\t\n\t\t\t\t\tMSE with “sinusoidal” reference signal for Neutralization System
MSE with “sinusoidal” reference signal for Hybrid System
Another important is a narrow band signal, as explained before, is composed of the sum of narrow band sinusoidal signals of 100, 200, 400, and 600 Hz. Figures 31 to 33 show the results for this consideration
\n\t\t\t\t\tMSE with “4 tones” reference signal for Feedforward System
MSE with “4 tones” reference signal for Neutralization System
MSE with “4 tones” reference signal for Hybrid System
Finally, we use two recorded signals, corresponding to a "plane" and one to a "motor", meaning the evidence most relevant to our system. Of Figures 34 through 41, shows the convergence achieved with the proposed system.
\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\tFinally, it is important to consider that an ANC system should respond successfully to a change in the status of secondary path, which corresponds, for example, a possible movement of the microphone in a pipeline, or any vibration or change in of the system. Figures 24 and 25 show an abrupt change in secondary path at iteration 1000 [5]. We can observe that the behavior of both remain stable.
\n\t\t\t\t\tFigures 40 and 41 show selected results for the neutralization and hybrid systems, which are of greatest interest.
\n\t\t\t\t\tMSE with “Motor” reference signal for Feedforward System
MSE with “Motor” reference signal for Neutralization System
MSE with “Motor” reference signal for Hybrid System
MSE with “Airplane” reference signal for Feedforward System
MSE with “Airplane” reference signal for Neutralization System
MSE with “Airplane” reference signal for Hybrid System
MSE with “4 tones” reference signal for Neutralization System, considering changing secondary path
MSE with “4 tones” reference signal for Hybrid System, considering changing secondary path
The adaptive filtering is a powerful tool that offers various solutions to many fields of science today. This chapter shows the efficiency of the hybrid system in reducing electrical noise and noise currently present in conventional systems where noise becomes a significant cause of health problems, or a situation that can affect communications Internet or phone, to name a few.
\n\t\t\tAdaptive filtering, which has been successfully applied in the solution of several practical problems which main kinds are described some in this chapter, has relied mainly in the transversal filter structures. However, when the filter order becomes large, the transversal computational complexity and convergence rate may limit its capability for solving practical problems. This chapter presented an overview of the Hybrid System.
\n\t\t\tIn particular, there are few references about hybrid systems, those conjoined feature more traditional patterns such as a priori and a posteriori systems. Of course they inherit the problems of these two, but the advantage they offer is based on the robustness of such systems for signals of different characteristics as continuous, intermittent and impulsive, and we tested a hybrid system in two interesting and relevant scenarios: unwanted signals in the fields of acoustics and telephony.
\n\t\t\tThe proposed system works in an acceptable way for telephone echo problems, but it is necessary to consider and adjust the different parameters. The system is capable of cancelling echo of voice signals and can be applied to simulated scenarios of double talk without use the Double Talk Detector. Also it is necessary to evaluate the correlation between input signals since this correlation has a great impact of the performance of the system. If both signals are highly correlated, it is necessary to use a small step size for both feedback and feedforward systems. We established the double talk situation in telephony conversations as the test system for our Hybrid system including some talks simulating a real conversation.
\n\t\t\tWith respect to Acoustic Noise Reduction, it must be notice that the results presented for a real-value filter coefficients refer to only one specific type of duct. This means that the response could probably improve in a different environment or in a duct with different properties. This situation represents a problem for the designer of a hybrid ANC, because for each environment where the system is to be applied would be no need to identify accurately the parameters to achieve the desired response. However difficult, this may not be impossible to do, so there is still a lot of work to be done with hybrid ANC systems.
\n\t\t\tThis chapter discusses a new Hybrid Active Noise Control system and the impact adaptive filtering has on this field. The objective is to achieve improved performance at a reasonable computational cost in a Hybrid ANC system that considers two of the more important troubles of the ANC. We show two examples to prove the contribution of this system, one is a little generalist about cancelling several kinds of noise, and one very specific, which represents one persistent problem like telephone echo on telecommunications nowadays: networks have been modified by the use of new technologies and constant innovations have led to automate the process of interconnection of subscribers, and the inclusion of forms of streaming media.
\n\t\t\tTherefore, he was a rigorous analysis of the results and their parameters under the above considerations. The results show the relevance of hybrid systems for consideration in removing acoustic noise or echo in telephony, with tools of adaptive systems. The advisability of this hybrid system is a matter that must be analyzed in depth.
\n\t\tThis work was supported by the Department of Mechatronics, part of the School of Design, Architecture and Engineering, Tecnológico de Monterrey, Campus Ciudad de Mexico.
\n\t\tThe Gulf of California is one of the most important marine ecosystems in Mexico and one of the most productive and biodiverse in the planet, as well as being one of the least disturbed. There we find 922 islands [1] that stand out for their high diversity in species, its high level of endemic species and a great biological richness, features that have allowed these places to be considered as natural evolutionary laboratories [2]. Mollusks within the marine ecosystem play a big role in the energy flux and community structure, due to the fact that many of them work as ecological regulators [3, 4] and indicators of disruptions that take place in these systems [5]. Besides, they constitute an abundant and ecological important group due to the functions performed by each one of their members within the food web, nutrient recirculation and energy flux [6].
\nMollusks are mainly used in benthic studies to relate their presence/absence and/or dominance, with the aim to set their relationship with types of seabed and substrate [7]. Furthermore, they help to establish a baseline for future follow-up and evaluation programs [8]. Life cycles, a high level of stress tolerance [7], an intimate relationship with the sediment and a high response toward disturbances [9] make them ideal organisms to study natural and anthropogenic environmental changes [10, 11].
\nAs a framework, most of the published research about Mollusks in the Mexican Pacific has to do with faunistic studies and taxonomy, whereas others talk about diversity aspects and variation through time [12, 13, 14, 15, 16, 17]. Additional studies relate to distribution and abundance [18, 19, 20, 21, 22, 23, 24] and ecology [25, 26, 27]. Based on these previous studies, there is a lack of current information about the biology and ecology of the community of Mollusks in the intertidal zone from the islands of the Gulf of California; henceforth, it is necessary to do research that can increase and deepen the knowledge about the composition, abundance, and diversity of Mollusks.
\nThe Baja California Peninsula encloses the Gulf of California and is one of the most remote peninsular areas of the world. The gulf is a big semi-enclosed sea with more than 1100 km in length, 100–200 km in width, and with 258,593 km (99,843 mi2) of surface which comprises more than 9° of latitude which cross the Tropic of Cancer in its southern part, extending to Cabo Corrientes (Jalisco, Mexico). It is the home of more of 900 islands and islets; it gives place to a highly rich and diverse habitat region for the evolutionary forces which in turn shape its flora and fauna. The northeast part of the gulf covers around 60,000 km2 (24,000 mi2) of sea surface, it extends to 3° latitude, and it is a unique water body in many ways. The weather is very dry, with an annual rainfall of less than 100 mm. The array of average monthly air temperatures in the northern gulf is of 18°C. The northern gulf presents some of the biggest tides in the world. The annual tide (amplitude) in San Felipe and Puerto Peñasco comprises around 7 m and in the Delta of the Colorado River, at the highest part of the gulf reaches almost 10 m [28].
\nThe Ohuira lagoon connects itself with a 700-m-width cannel at Topolobampo Port. The Ohuira lagoon, with 125 km2 (12,500 has) of surface, was the river basin of an ancient canal of the Fuerte River, which extended through the Topolobampo Bay, discharging its waters into this port. It is an area of shallows that during the rain period presents a deep zone of variable location depending on the tides and sediment dragging and presents a branch system that connects it with Navachiste Bay. In total, the system has eight islands: five within the Ohuira lagoon: Patos, Bledos, Bleditos, Tunosa, and Mazocahui (I and II) [29]. The circulation of the maximum currents in the lagoon’s mouth is of 1.15 m s−1, and in the channels of 1.10 m s−1 [30].
\nMollusks are one of the zoological groups with more biological success, as much for its number of living species as for the habitat diversity they colonize [31]. Within the marine ecosystem, Mollusks play an important role in the energy flux and the community structure, due to the fact that many of them work as ecological regulators [32] and as disturbance indicators inside these systems [5]. In addition, they constitute an abundant and ecologically important group because of the role that each member performs within the food web, nutrient recycling and energy flux [6]. Inside this group, there are primary consumers, both herbivores and detritivores, second-level predators and specialized parasites, as well as opportunistic species, which indicates different answers to habitat modifications and pollution [33]. These organisms possess one of the most widespread distributions in the planet, ranging from the coastline to great sea depths [34]. The highest ability of Mollusks to adapt has given them a huge success along their evolution, and they have colonized terrestrial, damp and freshwater habitats [35], as far as deserts and polar areas, as well as the tropics and great sea depths [36], being widely studied due to their social and economic importance, as well as their commercial and nutritional values [37].
\nMany diverse studies about Mollusks have been undertaken in the Gulf of California. Nevertheless, the available information regarding the community structure of the group is scarce. Such investigations contribute important information because density variations from specific populations can be known in a specific period of time and locality, as well as the abundance and composition of a community within a natural gradient or when pollution or illness problems exist in the environment [38, 39]. In 2008, in the Guasave municipality, Sinaloa, Mexico, a Mollusk census was performed in the intertidal zone from La Mapachera, Tesobiate, La Huitussera, San Lucas, Guasayeye, Nescoco, El Metate and Las Chivas islands from the lagoon system known as Navachiste, in order to elaborate taxonomic lists and an intertidal species diagnosis. The collected Mollusks were located systematically in four classes (Gastropod, Bivalvia, Polyplacophora and Cephalopoda), 40 families and 81 species. Gastropods represented 59% with 24 families and 46 species, bivalves constituted 43% with 14 families and 34 species, polyplacophora comprised 3% with 2 families and 2 species and the remaining 1% corresponded to cephalopods with 1 family and 1 species [40].
\nIn previous studies held in 2014 in the intertidal rocky zone (beach and mangrove area) from the Ohuira and Topolobampo Bays (Ahome), Sinaloa, the collected organisms represented a highly important trophic phase. The biodiversity and distribution of the community of epibenthic invertebrates was composed by a specific richness (S) of 168 species, divided in 10 taxonomic groups: 3 porífera, 2 cnidarians, 2 platyhelminths, 35 annelids, 2 sipunculids, 74 mollusks, 46 crustaceans, 1 pycnogonida, 1 ectoprocta, and 2 echinoderms, where Mollusks were the most predominant group with 74 species. The dominant Mollusks species were Neritina sp., and Cerithium stercusmuscarum. The epibenthic distribution was influenced by salinity and organic matter, enhancing the differences in the Ohuira lagoon [41].
\nThe interest in studying biodiversity is linked to the lack of knowledge that exists over its magnitude, the processes that determine it and the constant loss due to human actions or climate change effects; thus, it is important to know and understand the processes that determine the abundance and distribution of biodiversity under different spatial and temporal scales in the gastropod species, as well as their transformation due to the environment [42, 43, 44, 45].
\nConsidering the period between October 2016 and 2017, organisms were collected by some of the authors from this present chapter in order to evaluate the biodiversity of Mollusks within the project named “Community structure of the Mollusks found in the islands of the north of Sinaloa, México” (Register number DSA/103.5/16/10277). Sampling stations were established in Patos (25°20′450″ N, 109°00′531″ W), Bledos (25°18¨350″ N, 109°00′458″ W), Bleditos (25°14′566″ N, 109°00′664″ W), Tunosa (25°15′785″ N, 109°00′924″ W) and Mazocahui (25°34′154″ N, 109°00′855″ W) islands in the Ohuira lagoon. To collect gastropod Mollusks we took as reference six quadrants of 1 m2 dimension in the zone exposed to the waves and three quadrants in the area not exposed to the tides. The organisms were collected from the sand, mud, silt-clay and rocky soil, which were representative from the study area. Thereupon, in soft substrates the harvest was made manually, and those organisms that were found adhered to rocky substrates were removed with a scraper, chisel or hammer. In addition, those organisms that were found at a greater depth were collected by snorkeling. The collected Mollusks were stored in plastic bags with their corresponding label, according to the type of sample method. The organisms were conserved in ice to be transferred to the biology lab at the Universidad de Occidente Unidad Los Mochis, Ahome, Sinaloa, Mexico. Taxonomic keys were used to identify the gastropod Mollusks [46, 47, 48, 49, 50, 51, 52, 53].
\nThe analysis of the community structure of gastropod Mollusks was based on ecological indexes that quantified the information given by the lagoon system, which were applied based on each island and whether the organisms were exposed or not to the tide. To represent the biodiversity of gastropods we used the following indexes:
\nThe species richness (S) was estimated by counting the number of species because it is the easiest way to measure biodiversity, since it is based on the number of species that are present without considering their importance. The abundance (A) was estimated by counting the number of organisms that were registered in each sampling station. The relative abundance (Pi) represented the existing relation between the organisms of a single species and the total number of organisms from all the species encountered, by using the following equation (Eq. (1)):
\nwhere ni is the number of organisms from the “i” species and N is the total number of organisms from all gastropod species.
\nTo identify the dominant species from the community we used the community dominance index (ID) (Eq. (2)) [27, 54]:
\nwhere Y1 is the abundance of the most common species, Y2 is the abundance of the species that occupied the second place in abundance, and N is sum of the abundance of all species.
\nIn accordance with the estimators, Pi, ID, H′, as well as with the dominance level, the main species for each island was determined. To represent the sui generis characteristic from the community, we analyzed jointly the abundance (A) and frequency (F) to establish four categories of species which are cataloged as (AF)—highly abundant and very frequent, (aF)—less abundant and highly frequent, (Af)—highly abundant and less frequent, and (af)—less abundant and less frequent [27].
\nThe Shannon-Wiener diversity ecology index measured the average uncertainty degree to predict to which species a randomly chosen individual could belong to within a collection (Eq. (3)) [27, 38, 55, 56]:
\nwhere Pi is proportional abundance of the “i” species.
\nPielou’s equity measured the proportion of the observed diversity from the maximum expected diversity. Its value ranges from 0 to 1, where 1 corresponds to those situations in which all species are equally abundant (Eq. (4)) [38]:
\nwhere H´: Shannon-Wiener’s diversity and H′max: maximum diversity.
\nSpecies diversity under conditions of maximum equity, in other words, the species diversity from a sample if all the species (S) had the same abundance equity (Eq. (5)):
\nThe diversity index or Margalef’s richness (Dmg), transformed the number of species per sample into a proportion in which species are added by the expansion of the sample. This index assumes that there is a functional relation between the number of species and the total number of organisms [38]:
\nwhere k is the constant.
\nIf the constant is not maintained, then the index varies with the sample size in an unknown manner. By using s-1 instead of S, we get Dmg = 0, when there is only one single species (Eq. (7)):
\nwhere S: number of species; and N: total number of organisms.
\nIn order to calculate these indexes the abundance data were transformed into a natural algorithm [27].
\nAt the Ohuira lagoon we collected a total of 5431 gastropods, being Patos Island the one with the highest abundance of 2135 organisms (39.35%), followed by Bleditos Island with 1471 (27.12%), Tunosa Island with 768 (14.14%), Bledos Island with 649 (11.95%), and Mazocahui Island with 408 organisms, representing 7.44%.
\nIn general, within all the islands that were studied in Ohuira lagoon a total of 22 species of gastropods were collected. In those areas where there was nonexposure to tides, the species that were found were: Cerithium stercusmuscarum (n = 333, Pi = 0.0613), Neritina sp. (n = 208, Pi = 0.0383), Nerita scabricosta (n = 301, Pi = 0.0554), Nerita funiculata (n = 207, Pi = 0.0381), Nassarius luteostoma (n = 22, Pi = 0.0041), Nassarius gallegosi (n = 20, Pi = 0.0037), Crucibulum spinosum (n = 217, Pi = 0.040), Eupleura sp. (n = 5, Pi = 0.000921), Crepidula onix (n = 1, Pi = 0.000184), Crepidula rostrata (n = 6, Pi = 0.001105), Fisurella sp. (n = 1, Pi = 0.000184), Littorina aspera (n = 5, Pi = 0.000921), Littorina modesta (n = 14, Pi = 0.0026), Crepidula lessoni (n = 10, Pi = 0.00184), Tegula corteziana (n = 5, Pi = 0.000921), Diodora sp. (n = 3, Pi = 0.00055), Scurria mesoleuca (n = 3, Pi = 0.00055), Diodora digueti (n = 3, Pi = 0.00055), Crucibulum scutellarum (n = 7, Pi = 0.00130), Murex (Recurvirostris) lividus (n = 3, Pi = 0.00055), Terebra sp. (n = 10, Pi = 0.00184), and Hexaplex (Muricanthus) nigritus (n = 10, Pi = 0.00184).
\nIn the areas where there was tidal exposure a total of 19 gastropod species were found: Cerithium stercusmuscarum (n = 704, Pi = 0.130), Neritina sp. (n = 271, Pi = 0.050), Nerita scabricosta (n = 319, Pi = 0.059), Nerita funiculata (n = 505, Pi = 0.0930), Nassarius luteostoma (n = 11, Pi = 0.0021), Crucibulum spinosum (n = 14, Pi = 0.0026), Crepidula onix (n = 10, Pi = 0.00184), Crepidula rostrata (n = 8, Pi = 0.0015), Littorina aspera (n = 1, Pi = 0.000184), Littorina modesta (n = 50, Pi = 0.0092), Crepidula lessoni (n = 69, Pi = 0.0127), Diodora digueti (n = 4, Pi = 0.00074), Murex (Recurvirostris) lividus (n = 11, Pi = 0.0021), Turritella gnostoma (n = 1, Pi = 0.000184), Thais biceralis (n = 1, Pi = 0.000184), Hexaplex (Muricanthus) nigritus (n = 557, Pi = 0.1030), Hexaplex eristrosthomus (n = 76, Pi = 0.0140), Phyllonotus brassica (n = 15, Pi = 0.0028), and Melongena patula (n = 10, Pi = 0.00184).
\nA total of 11 gastropod species were registered in Patos Island, where Cerithium stercusmuscarum showed the highest abundance with 214 organisms in the zone that was not exposed to the tide, whereas a total of 395 organisms were found in the area exposed to the tide. The least abundant species were Crepidula onyx, Crucibulum scutellatum, Nassarius gallegosi, Nassarius luteostoma, Littorina modesta, and Murex (recurvirostris) lividus, which were present with one single organism collected, both in the area exposed to the tide and the one not exposed to it (Figure 1).
\nDiversity and abundance of gastropod mollusks on islands of Ohuira lagoon.
Bledos Island was the one that showed a higher mollusk diversity with 13 species in which Cerithium stercusmuscarum was the most abundant with 41 organisms, whereas Nerita funiculata was the least abundant, being represented by only one collected individual (Figure 1).
\nBleditos Island had a gastropod diversity of 12 recorded species. Cerithium stercusmuscarum and Nerita scabricosta were the most abundant species in the intertidal area, being represented by 130 organisms. Crucibulum spinosum had 180 organisms in the area not exposed to the tide (Figure 1).
\nOn Mazocahui Island a total of 9 species were registered from which Nerita funiculata, and Neritina sp. had the highest abundance with 109 and 124 organisms, respectively in the intertidal area. On the other hand, Nassarius gallegosi (17 organisms) and Cerithium stercusmuscarum (26 organisms) had the highest abundance in the area not exposed to the waves (Figure 1).
\nTunosa Island had a diversity of 10 species, from which Nerita funiculata, Nerita scabricosta, and Hexaplex (Muricanthus) nigritus were the most abundant in both zones, the one exposed to the tide and the one not exposed to it, while Turritellla gnostoma, Thais biceralis, Hexaplex (Muricantus) nigritus, Crepidula onix, Crucibulum spinosum and Neritina sp. were the least abundant species in the area exposed to the tide (Figure 1).
\nCerithium stercusmuscarum (ID = 32.20%, AF, H´ = 0.3161) was found on five islands with 1037 collected organisms, being Isla Patos the island with the highest abundance and Mazocahui the one with the lowest abundance (35 organisms). Nerita funiculata and Nerita scabricosta were the most abundant species on Tunosa Island with 712 (ID = 24.53%, Af, H´ = 0.2662) and 620 (ID = 21.67%, Af, H´ = 0.2478) collected organisms, respectively, in the intertidal zone. Neritina sp. was the dominant species and presented the highest abundance on Patos Island with 479 collected organisms (ID = 13.07%, aF, H´ = 0.2142), the sum of the dominance of these species was of 91.47%, where 8.53% corresponds to the rest of the remaining gastropod species. The biometrics of the dominant species on the islands of the Ohuira lagoon, Ahome, Sinaloa, México were as follows: Cerithium stercusmuscarum with 26.65 ± 0.146 mm in length, Nerita funiculata with 16.03 ± 0.118 mm in length, Nerita scabricosta with 39.03 ± 1.46 mm in length, Neritina sp. with 8.9 ± 0.205 mm in length (Figure 2).
\nDominance of Cerathium stercusmuscarum, Nerita funiculata, Nerita scabricosta, and Neritina sp. on the islands of Ohuira lagoon, Ahome, Sinaloa, Mexico.
The gastropods Cerithium stercusmuscarum (J´1 = 0.5413, J´2 = 0.8390) was recorded on five islands with 1037 collected organisms, being Patos Island the one with the highest abundance and Mazocahui Island the one with the lowest (35 organisms), finding a higher tendency of the proportion of the observed diversity in those nonexposed areas. Nerita funiculata and Nerita scabricosta were the most abundant species on Tunosa Island with 712 (J´1 = 0.4677, J´2 = 0.8298) and 620 (J´1 = 0.6469, J´2 = 0.6739) respectively, recording the highest equity index in the areas exposed to the tides. Neritina sp. dominated with the highest abundance on Patos Island with 479 collected organisms (J´1 = 0.5831, J´2 = 0.6993) showing the same tendency of high equity in the nonexposed areas.
\nOn Patos Island we found Dmg = 1.80, on Bledos Island Dmg = 1.68, Bleditos Island Dmg = 1.53, Tunosa Island Dmg = 1.95, and on Mazocahui Island, Dmg = 1.81, which suggests that on Patos and Mazocahui Islands, the diversity or richness is similar, being higher on Tunosa Island and lower on Bleditos.
\nDue to the lack of biological information from the Gulf of California islands, specifically from the ones found in Ohuira lagoon and their ecological and economic importance, it is necessary to perform research to increase the knowledge about them and to contribute on the elaboration of management methods and alternatives for the sustainable use the marine resources found on the islands. While it is true that in the past years the number of investigations have increased, the marine studies that have been performed on the islands of the Ohuira lagoon do not provide enough information about the species that inhabit the area, such as their biology, ecology, reproduction, physiology and taxonomy. This is why this current research pretends to set a baseline for future studies of the gastropod mollusk community from these islands throughout time, in order to evaluate possible environmental changes whether they are natural or anthropogenic.
\nIn Ohuira lagoon, Ahome, Sinaloa, the ecological importance in particular of the species of gastropod Mollusks is related to trophic levels, since there are organisms that are of carnivorous feeding habits such as the black murex Hexaplex (Muricanthus) nigritus, the prince murex Hexaplex (Muricanthus) prínceps, the cabbage murex Phyllonotus brassica, the pink-mouthed murex Phyllonotus erythrostoma, Regal murex Phyllonotus regius, the Pacific melongena Melongena patula, the giant Eastern Pacific conch Strombus galeatus, and the Pacific cask shell Malea ringens, which can feed on other smaller gastropods such as Cerithium stercusmuscarum, the onyx slipper shell Crepidula onyx, Terebra armillata, Hormospira maculosa, and Fusinus (Barbarofusus) colpoicus, to mention some species. It is important to emphasize that both gastropods, the black murex Hexaplex (Muricanthus) nigritus and the ambiguous murex Hexaplex (Muricanthus) ambiguus, are sometimes considered as northern subspecies of the species radish murex Hexaplex (Muricanthus) radix [52]. Considering the gastropod species with the greatest economic-commercial importance in the study area, the biology is described for each case [41, 52].
\nThe distinctive features of the gastropod Hexaplex (Muricanthus) nigritus, are that it belongs to the family Muricidae, it has a relation of synonymy with Murex nigritus and Muricanthus nigritus; it has a very large, robust, bulbous shell with a moderately prominent conical spiral and a wide body turn. It presents six to nine strong spinal mandibular varices in the back of the body, crossed by spiral ribs intermixed with smaller ribs. It has relative scarce thorny acute varices, and those located on the shoulder and on the basis of the longer shell. It has a wide oval opening with a small rear channel and a wide siphoned channel, fairly well developed and slightly curved. It presents a strongly crenulated outer lip and an internal lip with a columellar adherent callus and a spiral crest on its back, and the nucleus of the operculum presents an anterior position. The color of the outer surface is white opaque, with a blackish-brownish dye on the ribs, spirals and thorns, and the opening is porcelain white. The maximum size reported was 150 mm, although the most common size is 120 mm. The reported habitats of the species were reefs or sandy bottoms in the intertidal zone and subcoastal shallow waters [52].
\nIt belongs to the Muricidae family, the synonyms used are Murex erythrostoma, Chicoreus erythrostoma, and Hexaplex erythrostoma. The distinctive features are a large, robust, globose-oval shell, with a short conical spiral and a wide body turn; four or five thick axial varices around the body, alternating with tubercular axial ridges; six to seven spiral crests that form nodules in the intervarical ridges and become open and sharp spines on the varices, being stronger in the shoulder; oval opening with a small posterior canal and a wide siphonel canal, relatively short and curved; an external erect and crenulated lip; an internal lip with a thin, expanded columellar callus and the nucleus of the operculum with an anterior position. The outer surface is opaque white and it has a bright pink opening. The maximum size reported was 150 mm, while the most common size is up to 100 mm. The habitat of the species was reported in sandy and muddy bottoms, both at low levels of the intertidal zone and offshore, up to 50 m deep [52].
\nWith only a single species in the study area, it belongs to the Melongenidae family. It presents a large and heavy, piriformed shell, the most recent rounds gradually enveloping the oldest, forming an irregular and deeply grooved suture and a very small spiral coil. Young organisms (less than 60 mm in length) are therefore more fusiform. The sculpture consists of a single-spaced row of short spines (although this feature might be absent) on the rounded shoulder, as well as numerous fine spiral grooves, mainly in the lower part of the shell. It has a rather smooth and thick periostraco, a very large opening, with a short and wide channel, an internal smooth and satin lip and a simple outer lip. The corneum operculum has a claw-like shape, with a terminal nucleus. The color is dark brown with cream spiral bands, just below the widest part of the last lap. The opening’s color is yellowish to pinkish. The families of gastropods with similar appearance present in the area are: Fasciolariidae, with more fusiform shells, longer and narrow siphon canals, with few folds sometimes present in the columella. The maximum reported size was 260 mm; nevertheless, the most common size was up to 160 mm. Its habitat is in sandbars and mud from the high levels of the intertidal zone. It is a carnivorous species that especially feeds on other gastropod Mollusks [52].
\nSeveral gastropods are used to create crafts (Port of Mazatlán, Sinaloa) such as jewelry boxes, picture frames, key holders, reliquaries, candles, lithographs, among others, by using shells of the gastropods belonging to the genus Hexaplex, Melongena, Phyllonotus, Strombus, Turritella, Crucibulum, Crepidula, and Cerathium. Mentioned artisan products are acquired by domestic and foreign tourists in local sales outlets established in municipal markets and in touristic areas. The elaboration of handcrafts has been carried out for decades mainly in the port of Mazatlán, where in many cases it becomes the livelihood-sustaining asset for a large number of families that take advantage of a waste product (shells) once the organism has been extracted for consumption and commercial importance. The same situation takes place with the smaller gastropods whose shells are collected on beach areas for these same purposes [10] (Figure 3a–d).
\n(a–c) Decorative articles made with shells of gastropods, simulating flowers; (d) jewelry boxes made with different species of gastropods; (e) capture of black murex Hexaplex (Muricanthus) nigritus by snorkeling on a working day in the lagoon Ohuira, Ahome, Sinaloa, and also the adhesion of masses of embryos (Me) on the shells of the organisms captured; (f) capture of gastropods Melongena patula (Mp), Hexaplex (Muricanthus) nigritus (HMn); and Phyllonotus erythrostoma in the study area; (g) “Chipped” processing of the capture of the gastropod Hexaplex (Muricanthus) nigritus in the study area.
Some organisms of the gastropod are a very important fishery resource worldwide and have a significant economic impact through the generation of resources at the level of artisanal fishermen, local trade and the export of fishery products of international value. The gastropod fishery destined for human consumption in the study area is based on the black murex Hexaplex (Muricanthus) nigritus, prince murex Hexaplex (Muricanthus) prínceps, cabbage murex Phyllonotus brassica, pink-mouthed murex Phyllonotus erythrostoma, Regal murex Phyllonotus regius, Pacific melongena Melongena patula, giant Eastern Pacific conch Strombus galeatus, and the Pacific cask shell Malea ringens [52].
\nThe fishery of the gastropods black murex Hexaplex (Muricanthus) nigritus (H. M. nigritus) is the one of greatest effort considering the abundance of the species, incidentally including another gastropod (prince murex Hexaplex (Muricanthus) prínceps) of the family Muricidae which has similar morphometric characteristics that go unnoticed to fishermen. Current official data from the port of Topolobampo, Sinaloa, on H. M. nigritus catches in the study area, with reference to the year 2008 with a catch of 8000 kg, and by 2014 of 4063 kg in live weight, which represented an income of $21,196.35 Mexican pesos [57, 58]. The exploitation and effort applicable to this gastropod in each season requires previous evaluations for each season according to the availability of the resource for each catch zone, due to their eating habits, the evaluation method can be by marking and recapture of marked organisms. The fishing effort is very variable, since not every year the catches are recorded. A fisherman by snorkeling can capture approximately 700 organisms in 4 h of work (Figure 3e). A minimum size for catching 90 mm of the shell [52] is contemplated in the Mexican legislation (Figure 3f–g). The average shell length recorded during the period 2016–2017 was 100 ± 2.53 mm, with a total weight of 104.45 ± 19.34 g. With regard to fisheries, growth with respect to the length ratio of the shell (mm)-total weight (g) was evaluated in black murex H. M. nigritus in the Ohuira lagoon and was represented by the potential model TW = 4E-06SL 3.7956, with R2 = 0.8317 (Figure 4a).
\nGrowth in length of the total weight (g)-shell of the (a) black murex Hexaplex (Muricanthus) nigritus and (b) pink-mouthed murex gastropod Phyllonotus erythrostoma in Ohuira lagoon, Ahome, Sinaloa, Mexico.
The pink-mouthed murex gastropod fisheries Phyllonotus erythrostoma (P. erythrostoma) in the study area is complemented by the gastropod cabbage murex Phyllonotus brassica and regal murex Phyllonotus regius which have similar morphometric characteristics that go unnoticed by fishermen [52]. There are currently no official data in the office of the Port of Topolobampo, Sinaloa on the catches of P. erythrostoma in the study area, the closest reference is to the year 2008, with a catch of 8000 kg, which represented an income of $ 11,096.21 Mexican pesos [57, 58, 59]. The exploitation and effort applicable to this gastropod in each season of capture, as in black murex H. M. nigritus, requires previous evaluations for each season according to the availability of the resource for each catch zone. Due to their eating habits the evaluation method can be made by labeling, and the recapture of marked organisms. The fishing effort is very variable, since not every year has a recorded catch. A fisherman by snorkeling can capture approximately 150 organisms during 4 h of work (Figure 3f). Growth with respect to the length ratio of the shell (mm)-total weight (g) was evaluated in pink-mouthed murex Phyllonotus erythrostoma in the Ohuira lagoon and was represented by the potential model TW = 0.5596SL 1.2287, with R2 = 0.4442 (Figure 4b).
\nCaptures in the study area of the Pacific melongena gastropod Melongena patula (M. patula), considering the official records in the Port of Topolobampo, Sinaloa, amounted 21,695 kg for the year 2014 with a value of $ 130,432 Mexican pesos. In contrast, the black murex gastropod H. M. nigritus has a lower abundance than M. patula but it is compensated with the longer shell length and total weight that also has its commercial value (Figure 3f). FAO in 1995 [52] reported a maximum shell length of 260 mm, with a common length of 160 mm. There are gastropods that have a shell length and total weight similar or superior to H. M. nigritus, P. erythrostoma, and M. patula like the giant eastern Pacific conch Strombus galeatus (Swainson, 1823) and the Pacific cask shell Malea ringens (Swainson, 1822). However, their catch is incidental because of their low abundance. For these species of gastropods, there are no official regulatory standards for their fisheries, it is only mentioned those non-updated catch volumes, as well as the recommended catch sizes in the national fisheries charter issued by the National Fisheries Institute, Mexico.
\nThe reproductive cycle of the snail Hexaplex (Muricanthus) nigritus, was studied in 2011, under lab conditions. A total of three females and two males were collected in Macapule lagoon, Guasave, Sinaloa, Mexico. After being held at water exchange regimes a total of 24 eggs masses were collected. The average number of capsules found within an eggs mass was of 150.75 ± 37.23. The estimated height and width for the capsules averaged 15.05 ± 1.21 and 4.93 ± 0.58 cm, respectively; the average number of embryos found per capsule was of 1583 ± 149, obtaining a total of 238,626 ± 3457 embryos in the egg mass. The obtained results were considered as useful tools to estimate the reproductive potential of H. M. nigritus for commercial and repopulation purposes [60].
\nA difference was found among the ecological indexes (H′, J′, Dmg) from the intertidal Mollusks community between the present study from the Ohuira lagoon, Ahome, Sinaloa (2016–2017 period) and previous studies undertaken at the Guasave municipality in Sinaloa (Navachiste lagoon) [15] and in the Topolobampo and Ohuira lagoons (mangrove zone) [16]. The abundance distribution of organisms and species on the collecting sites was heterogeneous. In the gastropod mollusk community in Ohuira lagoon, Ahome, there was a certain type of association with the type of substrate, which is composed of rocky and sandy zones (beach), zones with small rocks and in less proportion mangroves. The sampling methods showed that the gastropod Littorina modesta associates with the mangrove. In a previous study about epibenthic invertebrate communities associated with hard substrates in the intertidal zone in the Ohuira and Topolobampo lagoons, Sinaloa, the authors mentioned that the rocky intertidal zone and its organisms represent a very important trophic phase, and they recognize the importance of getting to know more about the biodiversity and distribution of the epibenthic invertebrate community of that study area. In their study, they performed 4 samplings with 50 × 50 cm quadrants at 5 stations from August 2011 to February 2012. The results showed that the community presented a specific richness (S) of 168 species, where 74 of them corresponded to Mollusks. The gastropod Cerithium stercusmuscarum was found within the dominant species, which matches with the results reported in the present study on the Ohuira islands [52]. The species Cerithium stercusmuscarum, Neritina sp., Nerita funiculata, Nerita scabricosta, Crucibulum spinosum, Nassarius luteostoma and Crepidula onix could be considered as representatives of the malacological fauna of the Ohuira lagoon, Ahome, Sinaloa, Mexico.
\nThe authors thank Dra. Mercedes Eugenia Guerrero Ruiz for translating the manuscript into English.
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