Four Short Courses on Harmonic Analysis: Wavelets, Frames, Time-Frequency Methods, and Applications to Signal and Image Analysis [Hardcover]

Introduction: Mathematical Aspects of Time-Frequency Analysis.- B-Spline Generated Frames.- Continuous and Discrete Reproducing Systems That Arise from Translations. Theory and Applications of Composite Wavelets.- Wavelets on the Sphere.- Wieners Lemma: Theme and Variations. An Introduction to Spectral Invariance and Its Applications.

From the reviews:

This is a well-written, advanced textbook on harmonic analysis intended for graduate students, mathematicians, and engineers working in signal processing and communications technology. The book is based on a number of lectures given at the summer school on New Trends and Directions in Harmonic Analysis, Approximation Theory, and Image Analysis...
???? The book is divided into five chapters, and each chapter concludes with a number of exercises of varying complexity. The first chapter contains a general introduction to the topic and to the terms used in the subsequent four chapters.
???? The specific topics covered in Chapters 25 are:? frames and bases in mathematics and engineering, wavelets with composite dilation and their applications, wavelets on the sphere and their applications, and finally Wiener's Lemma: theme and variations.?? Mathematical Reviews

The authors introduce the reader to their recent work in new areas of harmonic analysis. & The treatment of each topic is primarily mathematical, mostly targeting pure mathematicians and mathematical physicists in the fields of image and signal processing. & As an engineer, I found the book helpful in providing mathematical basis/direction for new techniques in time-frequency analysis of signals. (Menachem Rafaelof, Noise Control Engineering Journal, Vol. 58 (5), September-October, 2010)

The present texts consists of four lectures on recent topics in time-frequency analysis which grew out of a summer school, together with an introductory chapter with backgroulÍ