## Fast Transforms: Algorithms, Analyses, ApplicationsThis book has grown from notes used by the authors to instruct fast transform classes. One class was sponsored by the Training Department of Rockwell International, and another was sponsored by the Department of Electrical Engineering of The University of Texas at Arlington. Some of the material was also used in a short course sponsored by the University of Southern California. The authors are indebted to their students for motivating the writing of this book and for suggestions to improve it. |

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### Contents

Fourier Series and the Fourier Transform | 6 |

Discrete Fourier Transforms | 33 |

Fast Fourier Transform Algorithms | 58 |

Copyright | |

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### Common terms and phrases

4-point DFT 8-point additions aliased amplitude analog filter arithmetic operations bandwidth basis functions Chapter circular convolution circular shift computation data sequence decimation defined delta functions demodulator developed DFT coefficients DFT matrix DFT output digital filter dyadic entry Equation equivalent evaluation example fast algorithms filter output FIR filter Fourier series Fourier transform frequency domain given gives GT)r implementation integer inverse K. R. Rao Kronecker product magnitude mainlobe matrix factors matrix of exponents mixed radix modulo noise nonperiodic number of multiplications octave passband polynomial transforms power spectrum prime number primitive root Problem proportional filters recursive reduced representation respectively sampled-data sampling Section sequence number shaped DFT filter shift matrix Show shown in Fig Signal flowgraph sinusoids sparse matrix Table theorem transform sequence twiddle factors values vector Walsh functions waveforms WHT)h window word length yields zero