Open access peer-reviewed Edited Volume

Recent Advances of Wavelet Transform and Their Applications

Francisco Bulnes

Investigación Internacional Avanzada en Matemáticas e Ingeniería (IINAMEI)

A pioneering researcher in mathematical nanotechnology, spectral curvature theory, and research theory. He has many mathematics theorems, math objects, and new concepts in theoretical physics attributed to his name. He is the appointed head of the IINAMEI and research head in TESCHA. Dr. Bulnes received the Doctor Honoris Causa in Education Philosophy and Peace Ambassador prize by ODAEE in Frankfurt, Germany. He is also a distinguished member of the Czech Republic Mathematics Society (JCFM).

Covering

Complex Wavelet Transform Morlet Wavelet Transform Wavelet Prediction Image Wavelet Decomposition Spectrometry Mexican Hat Wavelet Haar Wavelet Daubechies Wavelet Triangular Wavelet Data Series Time Series S-Transform

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About the book

In the last years, different versions of wavelet transforms (continuous, discrete, real, and complex) have revolutionized the managing of spectral data and computing data related to the multi-resolution analysis, graph representation in trees to sub-representation of spectral bands in wavelets decomposition to an image, time-series data to localization of time meaning signals, spectrometry and spectrograms data, etc. The applications are diverse and are focused on the complementation of the Fourier transforms data in its spectral image as well as slight benefits over Fourier transforms in reducing computations when examining specific frequencies. Despite its major advantages, we can interpret a two-dimensional spectral image related to Fourier analysis and dynamical systems in search for signals of a known, non-sinusoidal shape.

Such is the case, for example, with wavelets that have an important role in standard STFT/Morlet analyses. From a purely mathematical point, a wavelet series is a representation of a square-integrable (real- or complex-valued) function by certain orthonormal series generated by wavelets. An important fact to consider with these representations and their consistencies is the Riesz theorem and aspects of functional analysis related to the convergence of the different wavelet series that can be constructed and generated to start an appropriate wavelet. Also, related problems with wavelets and other functional transforms include, for example, the Mexican hat wavelet, Haar Wavelet, Daubechies wavelet, triangular wavelet, and more.

Publishing process

Book initiated and editor appointed

Date completed: October 14th 2021

Applications to edit the book are assessed and a suitable editor is selected, at which point the process begins.

Chapter proposals submitted and reviewed

Deadline for chapter proposals: November 11th 2021

Potential authors submit chapter proposals ready for review by the academic editor and our publishing review team.

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Approved chapters written in full and submitted

Deadline for full chapters: January 10th 2022

Once approved by the academic editor and publishing review team, chapters are written and submitted according to pre-agreed parameters

Full chapters peer reviewed

Review results due: March 31st 2022

Full chapter manuscripts are screened for plagiarism and undergo a Main Editor Peer Review. Results are sent to authors within 30 days of submission, with suggestions for rounds of revisions.

Book compiled, published and promoted

Expected publication date: May 30th 2022

All chapters are copy-checked and typesetted before being published. IntechOpen regularly submits its books to major databases for evaluation and coverage, including the Clarivate Analytics Book Citation Index in the Web of ScienceTM Core Collection. Other discipline-specific databases are also targeted, such as Web of Science's BIOSIS Previews.

About the editor

Francisco Bulnes

Investigación Internacional Avanzada en Matemáticas e Ingeniería (IINAMEI)

Dr. Francisco Bulnes has a Ph.D. in Mathematical Sciences from the Instituto de Matemáticas, Universidad Nacional Autonoma de México (IM/UNAM). He is the director of Advanced International Research in Mathematics and Engineering (IINAMEI) and editor in chief of the journal Mathematics. Dr. Bulnes has authored more than 100 journal papers and several books in mathematics and physics research. He is a well-known pioneer and creator of theories, theorems, and math objects. He has received various honors and awards (Doctorates Honoris Causa) from universities and both governmental and non-governmental organizations. He has two post-doctorates in mathematics from Cuba and Russia. His scientific work has been published by different countries including Spain, China, the United States, Russia, Cuba, United Kingdom, México, and India where he has even been honored through tribute in a British publishing house.

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Book chapters authored 11

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