DESIGN OF DISCRETE-COEFFICIENT-VALUE LINEAR-PHASE FIR FILTERS WITH OPTIMUM NORMALIZED PEAK RIPPLE MAGNITUDE

The passband gain of a continuous-coefficient-value (infinite precision) filter may be arbitrarily scaled by scaling its coefficient values. Scaling the coefficient values corresponds to scaling the pass-band gain and peak ripple magnitude of the filter by the same scaling constant. Hence, the normalized peak ripple magnitude, i.e., peak ripple magnitude divided by passband gain, remains unchanged. However, this is not the case in the design of a discrete-coefficient-value filter, the coefficient values cannot be arbitrarily scaled and still maintain their discrete nature. Thus in the case of a discrete-coefficient-value filter, it is necessary to reoptimize the coefficient values when the passband gain is scaled if the normalized peak ripple magnitude of the filter is to be minimized. As a consequence, the normalized peak ripple magnitude changes as the passband gain changes. In this paper, we present several methods for the design of discrete-coefficient-value linear phase FIR filters with minimum normalized peak ripple magnitude. © 1990 IEEE