Fast Transformations and Kronecker Products

  • Manfred R. Schroeder
Part of the Springer Series in Information Sciences book series (SSINF, volume 7)


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).


Convolution Sino 


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  1. 17.1
    A. Hedayat, W. D. Wallis: Hadamard matrices and their applications. Ann. Statistics 6, 1184–1238 (1978)MathSciNetMATHCrossRefGoogle Scholar
  2. 17.2
    M. Harwit, N. J. A. Sloane: Hadamard Transform Optics ( Academic, New York 1979 )MATHGoogle Scholar
  3. 17.3
    H. J. Nussbaumer: Fast Fourier Transform and Convolution Algorithms (Springer,Berlin, Heidelberg, New York 1981 )MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Manfred R. Schroeder
    • 1
    • 2
  1. 1.Drittes Physikalisches InstitutUniversität GöttingenGöttingenFed. Rep. of Germany
  2. 2.Acoustics Speech and Mechanics ResearchBell LaboratoriesMurray HillUSA

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