Optimum Zonal Encoding of Digital Signals with Transforms

Digital signal compression by spectral transforms, known as zonal coding, is considered. We obtain an essential improvement of the bounds of [B. I. Golubov et al., Walsh Series and Transforms: Theory and Applications, Kluwer, Dordrecht (1991)] for the discrete Fourier transform spectrum on the class of Lipschitzian signals and for the mean-square signal reconstruction error on this class. A unified approach is proposed to the construction of spectral bounds of a real-valued orthogonal transform. This approach is applied to develop optimal zonal coding methods using some real trigonometric transforms, as well as Walsh and Haar transforms.