A Generalized Technique for Spectral Analysis

Authors:
Harry C. Andrews;Kenneth L. Caspari
Affiliations:
ITT Electro-Physics Laboratories, Inc., Hyattsville, Md./ Department of Electrical Engineering, University of Southern California, Los Angeles, Calif. 90007.;ITT Electro-Physics Laboratories, Inc., Hyattsville, Md.
Venue:
IEEE Transactions on Computers
Year:
1970

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Abstract

A technique is presented to implement a class of orthogonal transformations on the order of pN logp N operations. The technique is due to Good [1] and implements a fast Fourier transform, fast Hadamard transform, and a variety of other orthogonal decompositions. It is shown how the Kronecker product can be mathematically defined and efficiently implemented using a matrix factorization method. A generalized spectral analysis is suggested, and a variety of examples are presented displaying various properties of the decompositions possible. Finally, an eigenvalue presentation is provided as a possible means of characterizing some of the transforms with similar parameters.