The Algebraic Approach to the Discrete Cosine and Sine Transforms and Their Fast Algorithms

@article{Pschel2003TheAA,
  title={The Algebraic Approach to the Discrete Cosine and Sine Transforms and Their Fast Algorithms},
  author={Markus P{\"u}schel and Jos{\'e} M. F. Moura},
  journal={SIAM J. Comput.},
  year={2003},
  volume={32},
  pages={1280-1316}
}
It is known that the discrete Fourier transform (DFT) used in digital signal processing can be characterized in the framework of representation theory of algebras, namely as the decomposition matrix for the regular module C[Zn] = C[x]/(x − 1). This characterization provides deep insight on the DFT and can be used to derive and understand the structure of its fast algorithms. In this paper we present an algebraic characterization of the important class of discrete cosine and sine transforms as… CONTINUE READING
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