Abstract
Wavelets have attracted a lot of attention from people involved in time-frequency analysis of signals. The literature on wavelets, books, papers, is quite extensive. Many practical applications of wavelets have been found. Signals can be decomposed into wavelets, which capture frequency and time punctual characteristics of nonstationary signals, which is an important advantage compared with the Fourier transform. The first section of this chapter presents the Haar wavelet, being an important archetype of wavelet that also fits well with the introductory purpose of this section. Once a mathematical approach, in terms of functional decomposition, has been introduced, the second section deals directly with the heart of the matter: the multiresolution analysis equation. From this equation a series of different types of wavelets can be deduced, as it will be described in the third and fourth sections. Then, the next sections are devoted to the continuous wavelet transform, the lifting method, wavelet packets, and multiwavelets. There are two sections for experiments and applications, including signal denoising and compression. The final section introduces the MATLAB wavelet toolbox.
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Giron-Sierra, J.M. (2017). Wavelets. In: Digital Signal Processing with Matlab Examples, Volume 2. Signals and Communication Technology. Springer, Singapore. https://doi.org/10.1007/978-981-10-2537-2_2
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DOI: https://doi.org/10.1007/978-981-10-2537-2_2
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