Stability and Performance Comparisons of Infinite Impulse Response Digital Filters with Rounded Coefficients

This paper compares the stability and performance of several types of infinite impulse response digital filters as their coefficients are rounded to successive decimal places. A general purpose computer program is used, which is capable of determining stability and performance characteristics. The program has options for working in either the S or Z domain, as well as the ability to present the designer with a Nyquist plot of the proposed filter, a calculation of the gain and phase margin, a calculation of the filter\u27s bandwidth and ripple, and plots of filter performance. The program also determines the maximum amount of rounding the filter coefficients will tolerate before driving the system to instability, while providing the user with stability and performance plots for each step in the rounding process. The program was written in APL and is carefully documented with comments and detailed flowcharts. The program is then used to study the stability of two cases of filter design. The first case is a study of stability and its relation to filter transforms from the S to the Z domain. The second case is a comparison of stability and performance of two classes of filters as the order of the filter increases. In each case the gain margin, phase margin, bandwidth, and ripple will be plotted vs the decimal place where rounding has occurred