Time frequency and time scale methods : adaptive decompositions uncertainty principles and sampling 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. &nbsp; 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