Contents 1. INTRODUCTION
Discrete orthogonal transforms have been very useful for digital signal and image processing [1], [2], [11], [12], [13], [15]. Fast algorithms for efficient computation of discrete Fourier transform were particularly responsible for the enormous interests in its applications in digital signal processing. Other commonly used transforms are: Walsh Hadarmard Transform (WHT), Haar Transform (HT), Karhuneu-Loeve transform (KLT) and discrete Cosine transform (DCT). The WHT is a fairly simple transform and has found many applications such as applications in data compression involving image transmission and storage, spectral techniques in logic design, etc. Among existing discrete transforms, HT has the lowest computational costs. The HT is useful in signal and image processing applications where real-time implementation is essential [11], [13]. The KLT is a statistically optimal transform as its transform matrix is diagonal, but it suffers from costly computation and generation of the transform [1], [2], [11], [13], The DCT has been widely utilized in many signal and image processing applications [11], [12], [13] and is a core of many multimedia standards. It has been shown that the statistical performance of DCT in generalized Wiener filtering is the closest to the optimal transform KLT [1], [11], [13]. When operating on the residual images at some bit rates, the DCT does not work significantly better than the simpler transforms such as the WHT or HT [4]. Hence there is a need of analyzing simpler mathematically transforms in various signal and image processing applications.