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Developed in this book are several deep connections between timefrequency (Fourier/Gabor) analysis and timescale (wavelet) analysis, emphasizing the powerful adaptive methods that emerge when separate techniques from each area are properly assembled in a larger context. While researchers at the forefront of these areas are well aware of the benefits of such a unified approach, there remains a knowledge gap in the larger community of practitioners about the precise strengths and limitations of Fourier/Gabor analysis versus wavelets. This book fills that gap by presenting the interface of timefrequency and timescale methods as a rich area of work. 'Foundations of TimeFrequency and TimeScale Methods' will be suitable for applied mathematicians and engineers in signal/image processing and communication theory, as well as researchers and students in mathematical analysis, signal analysis, and mathematical physics.
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