Invariant Spaces and Cosine Transforms
Bozhan Zhechev
Institute of Computer and Communication Systems, 1113 Sofia,
E-mail: jechev@agatha.iac.bg
Abstract: The discrete cosine (and sine) transforms (DCT/DST) are analyzed in
this paper on the basis of the linear representations of finite groups and geometrical
approach. These transforms are extremely useful for multirate systems, adaptive filtering
and compression of speech signals and images. It is shown that if the Discrete Fourier
Transform (DFT) operator is referred to an appropriate basis it takes a block-diagonal form.
These blocks coincide with DCT-1/DST-1 for even dimensions of signals space and with
DCT-5/DST-5 for odd ones. The results enable the investigation of the full structure of DCT/DST.
Keywords: cosine transforms, orthogonality, signal processing, fast transforms,
filter banks, characters of groups, theory of groups.