Linear sequential coding of random space-time fields

A random signal observed in additive noise is to be linearly preprocessed for transmission via a channel of dimensionality less than that of either the observations or the signal. At the receiver, the signal is to be linearly reconstructed under a weighted-mean-square-error criterion. It is shown that there is no loss of overall optimality if the operation on the raw observations is partitioned into an optimal (least mean-square-error) prefilter followed by a linear coder.

A proof of the separability of prefiltering and coding (Corresp.)

The basic problem considered in this thesis is how to discretize a random process observed at one end, and after transmission, to reconstruct the desired signal from the discretized data received at the other end. The discretizing process consists of sampling, quantization and a presampling operation. The system under consideration in this work can either be regarded as a data communication or a data processing system. The main purposes of this work are: 1. To solve for the optimal realizable pre-transmission filter (prefilter) at one end, and the optimal realizable reconstruction filter (postfilter) at the other end using a state-space representation and the innovations approach. 2. To investigate the functions of the optimal realizable preand postfilters in comparison with that of the optimal unrealizable filters. 3. To investigate the smoothing problem as a function of allowable delay. The major contributions of this work are: 1. The state-space and innovations approach has been successfully applied to derive the optimal realizable zero-lag pre-and postfilters. The initial step in the procedure is to find the optimal post (pre) filter with a given pre (post) filter. Joint optimization then is carried out for the special case in which the quantization noise and channel additive noise are absent. The optimal filters are specified as solutions to differential equations in the state variables. 2. In the absence of the optimal prefilter, the optimal finite-lag postfilter has been found. An error-reduction factor and a delay-efficiency factor have been defined in order to study the effect of introducing delay on reducing the error between the output of the system and the desired signal. 3. Numerical examples of the performances of various systems have been worked out, and interpretations are given. A STATE-SPACE APPROACH TO THE DESIGN OF PREAND POSTFILTERS IN A SAMPLED-DATA COMMUNICATION SYSTEM by YERN YEH A thesis submitted to. the Graduate Faculty in partial fulfillment of the requirements for thedegree of DOCTOR OF PHILOSOPHY * in Electrical Engineering

A state-space approach to the design of pre- and postfilters in a sampled-data communication system

A state-space approach to optimum postfiltering of sampled data

A state-space formulation of the causal linear prefiltering problem in sampled-data systems

Optimal (least-mean-square linear) filtering of random signals prior to sampling may be represented as a Wiener-Kalman state-variable filter followed by a coder that synthesizes the signal to be sampled as a linear combination of the estimated states. Although the prefilter doubles the number of states of the overall presampling signal process, the postsampling reconstruction filter need only model the original signal generator and the coder. Overall optimization involves selecting the parameters of the coder to minimize a weighted time-averaged error criterion.

D. Petersen

Papers

Reexamination of the prefiltering problem in a state-variable formulation (Corresp.)