Predictive transform for optimum digital signal processing

A unified approach to optimum digital signal modeling, coding, estimation, and control is outlined. The origins of the proposed technique reside in a minimum-mean-square-error predictive transform (PT) coding formulation which yields a decoder that is a whitening PT model of the source whose output is to be encoded. This PT decoder is integrated with Kalman estimation (prediction, filtering and smoothing) as well as linear quadratic Gaussian control to produce a comprehensive approach to estimation and control that directly addresses the signal modeling problem. An additional bonus of the proposed unified approach to optimum digital signal processing is that a transformation mechanism arises which leads to significant design and implementation simplifications when the dimension of the signal is large. These ideas are illustrated with a 2D monochrome image application, where it is found that the design and implementation requirements of a PT smoother are often much less than those of a Kalman smoother with strictly similar performance. Specifically, the design computational burden is often improved by a factor greater than four and the implementation complexity burden by a factor close to four