Synthesis of Optimal Filters for a Feedback Quantization System

One proposal for a base-band quantization system for narrow-band television signals incorporates linear predistortion and reconstruction, and a linear noise feedback loop around the quantizer. Using an additive noise model for the quantizer, a procedure is developed for synthesizing a predistortion filter ( ), a reconstruction filter ( ), and a feedback filter (F) for this system so as to minimize a quantity representing the subjective effects of over-all system errors. The feedback filter F is assumed to be a tapped delay line, whose tap weights are obtained through a rapidly converging iterative procedure on an IBM 7090 automatic computer. Explicit formulas are derived for the amplitude responses of the optimal and filters. The system functions for and are obtained through a least squares approximation program on the IBM 7090 computer. Based upon these system functions, passive, lumped parameter predistortion and reconstruction filters are designed.