Fourier analysis on finite groups with applications in signal processing and system design / Radomir S. Stanković, Claudio Moraga, Jaakko Astola.

Includes bibliographical references and index.

Signals and Their Mathematical Models -- Systems -- Signals -- Mathematical Models of Signals -- Fourier Analysis -- Representations of Groups -- Complete reducibility -- Fourier Transform on Finite Groups -- Properties of the Fourier transform -- Matrix interpretation of the Fourier transform on finite non-Abelian groups -- Fast Fourier transform on finite non-Abelian groups -- Matrix Interpretation of the FFT -- Matrix interpretation of FFT on finite non-Abelian groups -- Complexity of the FFT -- Complexity of calculations of the FFT -- Remarks on programming implementation of FFT -- FFT through decision diagrams -- Decision diagrams -- FFT on finite non-Abelian groups through DDs -- MTDDs for the Fourier spectrum -- Complexity of DDs calculation methods -- Optimization of Decision Diagrams -- Reduction Possibilities in Decision Diagrams -- Group-theoretic Interpretation of DD -- Fourier Decision Diagrams -- Fourier decision trees -- Fourier decision diagrams -- Discussion of Different Decompositions -- Algorithm for optimization of DDs -- Representation of Two-Variable Function Generator -- Representation of adders by Fourier DD -- Representation of multipliers by Fourier DD -- Complexity of FNADD -- Fourier DDs with Preprocessing -- Matrix-valued functions -- Fourier transform for matrix-valued functions -- Fourier Decision Trees with Preprocessing -- Fourier Decision Diagrams with Preprocessing -- Construction of FNAPDD -- Algorithm for Construction of FNAPDD -- Algorithm for representation -- Optimization of FNAPDD.

"Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design examines aspects of Fourier analysis on finite non-Abelian groups and discusses different methods used to determine compact representations for discrete functions providing for their efficient realizations and related applications. Switching functions are included as an example of discrete functions in engineering practice. Additionally, consideration is given to the polynomial expressions and decision diagrams defined in terms of Fourier transform on finite non-Abelian groups." "With nearly 100 illustrative figures and fifty tables, this is an excellent textbook for graduate-level students and researchers in signal processing, logic design, and system theory - as well as the more general topics of computer science and applied mathematics."--Jacket.