On the Equivalence Between One-Dimensional Discrete Walsh-Hadamard and Multidimensional Discrete Fourier Transforms

@article{Kunz1979OnTE,
  title={On the Equivalence Between One-Dimensional Discrete Walsh-Hadamard and Multidimensional Discrete Fourier Transforms},
  author={Henry O. Kunz},
  journal={IEEE Transactions on Computers},
  year={1979},
  volume={C-28},
  pages={267-268}
}
  • Henry O. Kunz
  • Published 1 March 1979
  • Computer Science
  • IEEE Transactions on Computers
It is shown that the discrete Walsh–Hadamard transform applied to 2none-dimensional data is equivalent to the discrete n-dimensional Fourier transform applied to the same 2ndata arranged on the binary n-cube. A similar relationship is valid for the generalized discrete Walsh transform suggested by Andrews and Caspari. This relationship explains the theorem concerning the shift invariance of the power spectrum for the Walsh–Hadamard transform and its generalizations. 
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References

SHOWING 1-8 OF 8 REFERENCES
Two-dimensional digital processing of one-dimensional signal
It is of importance to find the necessary and sufficient conditions under which the one-dimensional and two-dimensional processing of any general transform should be equivalent. These conditions areExpand
A Generalized Technique for Spectral Analysis
TLDR
It is shown how the Kronecker product can be mathematically defined and efficiently implemented using a matrix factorization method and a generalized spectral analysis is suggested, and a variety of examples are presented displaying various properties of the decompositions possible. Expand
B70-2 Transmission of Information by Orthogonal Functions
  • H. Andrews
  • Computer Science
  • IEEE Transactions on Computers
  • 1970
The book provides a new and interesting approach to the field of information and communication theory and is a welcome and thought- provoking exposition on a subject too often reviewed byExpand
Theory and Application of Digital Signal Processing
TLDR
In this well-written book, Bellman and Wing have indeed accomplished the task of introducing the simplicity of the invariant imbedding method to tackle various problems of interest to engineers, physicists, applied mathematicians, and numerical analysts. Expand
Orthogonal Transforms for Digital Signal Processing