Fast Convolution Algorithms
The main objective of this chapter is to focus attention on fast algorithms for the summation of lagged products. Such problems are very common in physics and are usually related to the computation of digital filtering processes, convolutions, and correlations. Correlations differ from convolutions only by virtue of a simple inversion of one of the input sequences. Thus, although the developments in this chapter refer to convolutions, they apply equally well to correlations.
KeywordsDigital Filter Chinese Remainder Theorem Cyclotomic Polynomial Fast Fourier Transform Method Circular Convolution
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- 3.1T. G. Stockham: “Highspeed Convolution and Correlation”, in 1966 Spring Joint Computer Conf., AFIPS Proc. 28, 229–233Google Scholar
- 3.3R. C. Agarwal, J. W. Cooley: “New Algorithms for Digital Convolution”, in 1977 Intern. Conf., Acoust., Speech, Signal Processing Proc., p. 360Google Scholar
- 3.4I. J. Good: The relationship between two fast fourier Transforms. IEEE Trans. C-20, 310–317 (1971)Google Scholar
- 3.5R. C. Agarwal, J. W. Cooley: New algorithms for digital convolution IEEE ASSP-25, 392–410 (1977)Google Scholar
- 3.6H. J. Nussbaumer: “New Algorithms for Convolution and DFT Based on Polynomial Transforms”, in IEEE 1978 Intern. Conf. Acoust., Speech, Signal Processing Proc., pp. 638–641Google Scholar
- 3.8R. C. Agarwal, C. S. Burrus: Fast one-dimensional digital convolution by multidimensional techniques. IEEE Trans. ASSP-22, 1–10 (1974)Google Scholar
- 3.10A. Croisier, D. J. Esteban, M. E. Levilion, V. Riso: Digital Filter for PCM Encoded Signals, US Patent 3777130, Dec. 4, 1973Google Scholar
- 3.12D. E. Knuth: The Art of Computer Programming, Vol. 2, Semi-Numerical Algorithms ( Addison-Wesley, New York 1969 )Google Scholar