Abstract
While on the subject of fast computational algorithms based on the Chinese Remainder Theorem and primitive roots (discussed in the preceding chapter), we will now take time out for a glance at another basic principle of fast computation: decomposition into direct or Kronecker products. We illustrate this by showing how to factor Hadamard and Fourier matrices — leading to a Fast Hadamard Transform (FHT) and the well-known Fast Fourier Transform (FFT).
“It is important for him who wants to discover not to confine himself to one chapter of science, but to keep in touch with various others.”
— Jacques Hadamard
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References
A. Hedayat, W. D. Wallis: Hadamard matrices and their applications. Ann. Statistics 6, 1184–1238 (1978)
M. Harwit, N. J. A. Sloane: Hadamard Transform Optics (Academic, New York 1979)
H. J. Nussbaumer: Fast Fourier Transform and Convolution Algorithms (Springer, Berlin, Heidelberg, New York 1981)
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© 1997 Springer-Verlag Berlin Heidelberg
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Schroeder, M.R. (1997). Fast Transformation and Kronecker Products. In: Number Theory in Science and Communication. Springer Series in Information Sciences, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03430-9_17
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DOI: https://doi.org/10.1007/978-3-662-03430-9_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62006-8
Online ISBN: 978-3-662-03430-9
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