Residual Correlation for Generalized Discrete Transforms

We have undertaken a systematic investigation of the performance of a complete set of discrete orthogonal transforms Gr(n). The criterion of performance is that defined by Hamidi and Pearl, namely the Residual Correlation. This criterion measures the proportional correlation left in by a transform which is suboptimal, in the sense of not completely decorrelating the signal as in the case of the Karhunen-Loeve transform. The family of orthogonal transforms Gr(n), as defined by Ahmed and Rao, ranges from the discrete Walsh transform DWT, to the discrete Fourier transform DFT, as r varies from r = 0 to r = n - 1. Our study is applied to Markov-1 signals only.