Fast Algorithms for Digital Signal ProcessingIntroduction to abstract algebra. Fast algorithms for short convolutions. Fast algorithms for the discrete Fourier transform. Number theory and algebraic field theory. Computation in surrogate fields. Fast algorithms and multidimensional convolutions. Fast algorithms and multidimensional transforms. Architecture of filters and transforms. Fast algorithms based on doubling strategies. Fast algorithms for solving Toeplitz systems. Fast algorithms for Trellis and tree search. A collection of cyclic convolution algorithms. A collection of Winograd small FFT algorithms. |
Contents
Introduction | 1 |
Introduction to Abstract Algebra | 20 |
Fast Algorithms for Short Convolutions | 65 |
Copyright | |
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2-point a₁ Berlekamp-Massey algorithm called Chinese remainder theorem coefficients columns complex field complex multiplications complex numbers components compute construct Cooley-Tukey FFT cyclic convolution algorithm cyclotomic polynomials d₁ d₂ defined deg f(x denoted digital signal processing discrete Fourier transform equal equations Euclidean algorithm factor fast FFT algorithms field element field F FIGURE filter section finite FIR filter G₁ Galois field GF(p given Good-Thomas Hence input data integers inverse iteration Kronecker product linear convolution method minimal polynomial mod p(x mod x² modulo multidimensional multiplica nesting node nonzero number of additions number of multiplications Number of Real output path polynomial transform postadditions prime polynomial problem procedure Proof radix-two real additions real multiplications real numbers recursive relatively prime ring rows S₁ sequence shift register shown in Fig T₁ tions Toeplitz matrix trellis two-dimensional Fourier transform V₁ vector Viterbi algorithm Winograd FFT Winograd small FFT zero αι