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).


Fast Fourier Transform Kronecker Product Primitive Root Hadamard Matrice Hadamard Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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

Personalised recommendations