Time frequency and time-scale methods

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Developed in this book are several deep connections between time-frequency (Fourier/Gabor) analysis and time-scale (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 developments in time-frequency and time-scale analysis 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 time-frequency and time-scale methods as a rich area of work. TOC:Preface.- Wavelets: Basic properties, parametrizations and sampling.- Derivatives and multiwavelets.- Sampling in Fourier and wavelet analysis.- Bases for time-frequency analysis.- Fourier uncertainty principles.- Function spaces and operator theory.- Uncertainty principles in mathematical physics.- A Appendix.- References.- Index