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 (
H_1
), a reconstruction filter (
H_2
), 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
H_1
and
H_2
filters. The system functions for
H_1
and
H_2
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.