A comrade-matrix-based derivation of the eight versions of fast cosine and sine transforms

  • Authors:

  • Alexander Olshevsky;Vadim Olshevsky;Jun Wang

  • Affiliations:

  • Department of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia;Department of Mathematics, University of Connecticut, Storrs, Connecticut;Department of Computer Science, Georgia State University, Atlanta, Georgia

  • Venue:
  • Contemporary mathematics
  • Year:
  • 2001

Quantified Score

Hi-index 0.00

Visualization

Abstract

The paper provides a full self-contained derivation of fast algorithms to compute discrete Cosine and Sine transforms I - IV. For the Sine I/II and Cosine I/II transforms a unified derivation based on the concept of the comrade matrix is presented. The comrade matrices associated with different versions of the transforms differ in only a few boundary elements; hence, in each case algorithms can be derived in a unified manner. The algorithm is then modified to compute Sine III/IV and Cosine III/IV transforms as well. The resulting algorithms for the versions III/IV are direct and recursive, such algorithms were missing in the existing literature. Finally, formulas reducing Cosine and Sine transforms of the types III and IV to each other are presented.