the discrete cosine transform dct-4 and dct-8
In paper two types of the discrete cosine (end sine) transforms (DCT/DST) are analyzed on the base of the linear representations of finite groups and geometrical approach. This transforms are useful for multirate systems, adaptive filtering and compression of speech signals and images. It is shown that if an operator, connected with the Discrete Fourier Transform (DFT), is referred to an appropriate basis it takes bloc-diagonal form. These blocks coincide with DCT-4/DST-4 for even dimensions of the signals' space and with DCT-8/DST-8 for odd ones. The results allow the full structure of the DCT/DST to be investigated end fast realizations to be construct.
cosine transforms signal processing filter banks fast transforms orthogonality