Iterative design of optimum filters for non mean-square-error performance criteria

In an earlier paper, the design of filters by means of an iterative adjustment scheme was described. The filter was assumed to be of a fixed form but to contain variable parameters. The problem is to find the parameter setting that minimizes the expectation of some weighted value of the error. The adjustment scheme was proposed because it has two advantages over present analytic techniques: 1) the error-weighting function may be any convex function rather than being restricted to the square: 2) the method does not require preliminary measurement of correlation functions or other statistics. The work presented in the previous paper was deficient in two respects: 1) it required that the adjustable parameters take on only quantized values rather than being continuously variable; 2) the rate of convergence presented there was slower than that actually obtainable. Section II of this paper presents the results of work that has eliminated both of these difficulties. Section III presents a scheme for continuously adjusting the filter parameters and proves that, under reasonable conditions, the parameter setting converges to the optimum. The advantage of this continuous-adjustment scheme over the one previously described is that it may be realized with only simple analog equipment.