# Fast Fourier Transform - Algorithms and Applications

Springer Science & Business Media, Feb 21, 2011 - Mathematics - 426 pages

Fast Fourier Transform - Algorithms and Applications presents an introduction to the principles of the fast Fourier transform (FFT). It covers FFTs, frequency domain filtering, and applications to video and audio signal processing.

As fields like communications, speech and image processing, and related areas are rapidly developing, the FFT as one of the essential parts in digital signal processing has been widely used. Thus there is a pressing need from instructors and students for a book dealing with the latest FFT topics.

Fast Fourier Transform - Algorithms and Applications provides a thorough and detailed explanation of important or up-to-date FFTs. It also has adopted modern approaches like MATLAB examples and projects for better understanding of diverse FFTs.

Fast Fourier Transform - Algorithms and Applications is designed for senior undergraduate and graduate students, faculty, engineers, and scientists in the field, and self-learners to understand FFTs and directly apply them to their fields, efficiently. It is designed to be both a text and a reference. Thus examples, projects and problems all tied with MATLAB, are provided for grasping the concepts concretely. It also includes references to books and review papers and lists of applications, hardware/software, and useful websites. By including many figures, tables, bock diagrams and graphs, this book helps the reader understand the concepts of fast algorithms readily and intuitively. It provides new MATLAB functions and MATLAB source codes. The material in Fast Fourier Transform - Algorithms and Applications is presented without assuming any prior knowledge of FFT. This book is for any professional who wants to have a basic understanding of the latest developments in and applications of FFT. It provides a good reference for any engineer planning to work in this field, either in basic implementation or in research and development.

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### Contents

 Introduction 2 Discrete Fourier Transform 5 Fast Algorithms 41 Integer Fast Fourier Transform 111 TwoDimensional Discrete Fourier Transform 127 VectorRadix 2DFFT Algorithms 185 Nonuniform DFT 194 Applications 235
 Integer Discrete Cosine Transform INTDCT 333 DCT and DST 349 Kronecker Products and Separability 363 Mathematical Relations 367 Basics of Matlab 369 Appendix H 379 Bibliography 383 Index 415

 Performance Comparison of Various Discrete Transforms 317 Spectral Distance Measures of Image Quality 325