The paper considers the first wavelet transform -- Haar one, and its connection with the orthogonal bases of the null spaces of cyclic endomorphisms -- filters. It is presented a new transform connected with the Haar transform through a bit-reversal matrix. This approach gives new possibilities of constructing fast transforms, especially a Fourier one.
In paper two types of the discrete cosine (and sine) transforms (DCT/DST) are analyzed. These transforms are useful for many applications. It is shown that if an operator, connected with the Discrete Fourier Transform (DFT), is referred to an appropriate basis it takes block-diagonal form. These blocks coincide with DCT-2/DST-2 for even dimensions of the… (More)