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.- Wiener’s 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
2–5 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 background material by the editors. … All chapters are well
written and provide a good introduction to their respective
subjects. … In summary, it is a good starting point for students
with a basic background in harmonic analysis as well as for
researchers working in this area.” (G. Teschl, Monatshefte für
Mathematik, Vol. 162 (4), April,2011)
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