Orthogonal transforms for digital signal processing

A tutorial-review paper on discrete orthogonal transforms and their applications in digital signal and image (both monochrome and color) processing is presented. Various transforms such as discrete Fourier, discrete cosine, Walsh-Hadamard, slant, Haar, discrete linear basis, Hadamard-Haar, rapid, lower triangular, generalized Haar, slant Haar and Karhunen-Loêve are defined and developed. Pertinent properties of these transforms such as power spectra, cyclic and dyadic convolution and correlation are outlined. Efficient algorithms for fast implementation of these transforms based on matrix partitioning or matrix factoring are presented. The application of these transforms in speech and image processing,…