In spectral representations of discrete functions, the main optimization goal is to reduce the number of non-zero spectral coefficients of the function that is represented as a linear combination of a set of basis functions. Fourier transform for matrix-valued functions provides a deterministic way to redistribute the complexity of a spectral representation into a small set of matrix-valued coefficients.
Citation:
Radomir S. Stankovic, Claudio Moraga, Jaakko Astola, "Remarks on the Structure of Matrix-Valued Spectral Transforms on Finite Non-Abelian Groups," ismvl, pp.188-193, 35th International Symposium on Multiple-Valued Logic (ISMVL'05), 2005