RADOMIR S.STANKOVIC – FOURNIER ANALYSIS ON FINITE GROUPS WITH APLICATIONS IN SIGNAL PROCESSING AND SYSTEM DESIGN

There are applications of Fourier analysis on finite non-Abelian groups.

The majority of publications in the field consider the Fourier transform. Non-Abelian groups have advantages in the implementation of spectral methods.

The analysis of finite groups with applications in signal processing and system design. The analysis of finite non-Abelian groups is examined and the methods used to determine compact representations are discussed. The example of switch functions is included in engineering practice. The decision diagrams are defined in terms of the Fourier transform on finite non-Abelian groups.

A review of signals and their mathematical models is the beginning of the topic. The book looks at recent achievements and discoveries.

• Matrix interpretation of the fast Fourier transform
• Optimization of decision diagrams
• Functional expressions on quaternion groups
• Gibbs derivatives on finite groups
• Linear systems on finite non-Abelian groups
• Hilbert transform on finite groups

An in-depth coverage of applications of abstract harmonic analysis on finite non-Abelian groups is one of the highlights. Each chapter has a list of references to help develop specialized courses or self-study.

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.

TABLE OF CONTENTS

Preface.

Acknowledgments.

Acronyms.

There are 1 signals and their mathematical models.

There are 1.1 systems.

There are 1.2 signals.

There are mathematical models of signals.

There are references.

The analysis is called a Fourier analysis.

There are representations of groups.

2.1.2 Complete Reducibility.

The function on finite groups.

There are 2.3 properties of the Fourier transform.

Interpretation of the Fourier Transform on Non-Abelian Groups.

2.5 Fast Fourier transform on non-Abelian groups.

There are references.

The FFT has 3 matrix interpretations.

There is a matrix interpretation of FFT on non-Abelian groups.

There are illustrations of examples.

The FFT has a complexity.

The FFT has a complexity of calculations.

There are Remarks on Programming Implememtation of FFT.

3.4 FFT through decision diagrams.

Decision Diagrams.

3.4.2 FFT on Finite Non-Abelian Groups.

The MMTDs are for the spectrum.

The calculation methods are complex.

There are references.

There are 4 Optimization of Decision Diagrams.

There are reduction possibilities in the decision diagram.

Theoretic Interpretation ofDD.

There are 4.3 decision diagrams.

The decision trees are called the Fourier Decision Trees.

There are 4 decision diagrams.

There is a discussion of different compositions.

4.4.1 is an approximation of the problem.

The two-variable function generator has a representation.

There is a representation of adders.

There is a representation of Multipliers.

There is a complexity of NADD.

Preprocessing with the 4th and 5th digits of the tyke’s tyke’s tyke’s tyke’s tyke’s tyke’s tyke’s tyke’s tyke’s

The functions are matrix-valued.

The Fourier transform is used for matrix-valued functions.

Preprocessing is used in the 4.10 Fourier Decision Trees.

Preprocessing with the Fourier Decision Diagrams.

The construction of FNAPDD.

4.13 is an example of a construction of FNAPDD.

There is a method for representation.

FNAPDD is the topic of 4.14 Optimization.

There are references.

There are 5 functional expressions on quaternion groups.

There are finite dyadic groups.

There are Finite Dyadic Groups.

There are 5 Fourier expressions on Q. 2 .

The expressions are called Arithmetic Expressions.

Walsh expansion expressions have a number of numbers.

The numbers on expressions Q. 2 .

There are Arithmetic-Haar expressions.

There are two Arithmetic-Haar expressions.

There are different polarity polynomials.

C(Q) has fixed- polarity Fourier expressions. 2 ).

Fixed-Polarity Arithmetic-Haar expressions are used.

There is a calculation of the Arithmetic-Haar Coefficients.

There is a FFT-like Algorithm.

There is a Calculation of Arithmetic-Haar Coefficients through Decision Diagrams.

There are references.

There are 6 gibbs derivatives on finite groups.

There is a definition and properties of gibbs derivatives.

There is an anti-Derivative.

There are partial gibbs derivatives.

There are 6.4 Gibbs Differential Equations.

There is a matrix interpretation of gibbs derivatives.

There are fast computations for calculation of gibbs derivatives on finite groups.

The calculation of gibbs derivatives is complex.

There is a calculation of gibbs derivatives.

There is a calculation of partial gibbs derivatives.

There are references.

There are 7 linear systems.

There are Linear Shift-Invariant Systems on Groups.

There are linear shift-invariant systems.

There are derivatives and systems of linear systems.

There is a discussion.

There are references.

There is a Hilbert Transform on Finite Groups.

There are some results of the analysis.

The non-Abelian groups have a Hilbert Transform.

There is a Hilbert Transform in Finite Fields.

There are references.

Index.

AUTHOR INFORMATION

STANKOVIC IS RADOMIR S. Professor, Department of Computer Science, Faculty of Electronics, University of Nis, Serbia.

There is a person named Clarice Moraga. Professor, Department of Computer Science, is based in Germany.

There is a man named Jakko T. Astola. Professor, Institute of Signal Processing, Tampere University of Technology, is a PhD.

You can get a fournier analysis on finite groups.

Free Fournier Analysis on Finite Groups with Aplications in Signal Processing and System Design is available.