Construction of Wavelets Through Walsh Functions

Description

This book focuses on the fusion of wavelets and Walsh analysis, which involves non-trigonometric function series (or Walsh–Fourier series). The primary objective of the book is to systematically present the basic properties of non-trigonometric orthonormal systems such as the Haar system, Haar–Vilenkin system, Walsh system, wavelet system and frame system, as well as updated results on the book’s main theme. Based on lectures that the authors presented at several international conferences, the notions and concepts introduced in this interdisciplinary book can be applied to any situation where wavelets and their variants are used. Most of the applications of wavelet analysis and Walsh analysis can be tried for newly constructed wavelets. Given its breadth of coverage, the book offers a valuable resource for theoreticians and those applying mathematics in diverse areas. It is especially intended for graduate students of mathematics and engineering and researchers interested in applied analysis. Front Matter ....Pages i-xxii Introduction to Walsh Analysis and Wavelets (Yu. A. Farkov, Pammy Manchanda, Abul Hasan Siddiqi)....Pages 1-25 Walsh–Fourier Series (Yu. A. Farkov, Pammy Manchanda, Abul Hasan Siddiqi)....Pages 27-78 Haar–Fourier Analysis (Yu. A. Farkov, Pammy Manchanda, Abul Hasan Siddiqi)....Pages 79-98 Construction of Dyadic Wavelets and Frames Through Walsh Functions (Yu. A. Farkov, Pammy Manchanda, Abul Hasan Siddiqi)....Pages 99-170 Orthogonal and Periodic Wavelets on Vilenkin Groups (Yu. A. Farkov, Pammy Manchanda, Abul Hasan Siddiqi)....Pages 171-234 Haar–Vilenkin Wavelet (Yu. A. Farkov, Pammy Manchanda, Abul Hasan Siddiqi)....Pages 235-252 Construction Biorthogonal Wavelets and Frames (Yu. A. Farkov, Pammy Manchanda, Abul Hasan Siddiqi)....Pages 253-282 Wavelets Associated with Nonuniform Multiresolution Analysis on Positive Half Line (Yu. A. Farkov, Pammy Manchanda, Abul Hasan Siddiqi)....Pages 283-315 Orthogonal Vector-Valued Wavelets on \(\mathbb {R}_{+}\) (Yu. A. Farkov, Pammy Manchanda, Abul Hasan Siddiqi)....Pages 317-358 Back Matter ....Pages 359-381