Non-causal representations of finite discrete signals

A theory of non-causal interpolative representation of finite discrete signals is developed. It is shown that such representations give lower mean square error, entropy and rate distortion compared to standard Markov representations. Compared to initial value Markov models, the non-causal models lead to stable boundary value problems. Relationship with Karhunen Loeve (KL) expansion and Innovation representation is established. An alternate interpretation of Wiener filter and a fast algorithm for KL transform of first order Markov sequence are given. Applications to image coding and filtering are discussed. Examples are given to illustrate the new results obtained.