## Number theory in digital signal processing |

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### Contents

The Discrete Fourier Transform and Circular Convolution | 3 |

Properties of the Cyclotomic Polynomials | 72 |

Introduction to Reprinted Papers | 79 |

Copyright | |

2 other sections not shown

### Common terms and phrases

Agarwal and Burrus algorithm for computing applications array calculation Chinese Remainder Theorem circular convolution coefficients Complex Mersenne Transforms complex numbers consider convolution algorithms convolved cyclotomic polynomials defined DFT's digital filtering digital signal processing dimension dimensional diminished-1 Discrete Fourier Transform divisor efficient equations example factor FFT algorithm fast Fourier transform Fermat number transform finite field FNT's formula GF(p hardware highly composite IEEE Trans input integers modulo inverse transform linear mapping matrix Mersenne prime method minimum number mod F modulo modulo F multi multidimensional multiplica mutually prime number of additions number of multiplications number theory obtain one-dimensional operations paper permutation polynomials post-weave prime factor FFT primitive root problem rectangular transform reduced representation residue reduction result ring of integers root of unity Section sequence subroutine subtraction Table techniques tion transform length values vector volution WFTA Winograd word length zero