A Fresh Revisit of the Issues and Improvements in Impulse Invariance Filter Design for Infinite Impulse Response Filters

The objective of this paper is to first present some issues with impulse invariance filter (IIF) design during the design of digital infinite impulse response (IIR) filters. Engineers are often confused about some inconsistent observations. For instance, if the impulse response of a digital filter is designed using the impulse invariance procedure, then the analog and digital filters’ frequency and step responses are very different. Two simple remedies are presented in this paper. One is a post-processing approach that scales the frequency and step responses of the digital filter by the sampling interval T. Another one is a pre-processing approach that scales the impulse response of the analog filter by T. However, even after these remedies, there is still a steady state bias in the step response of the digital filter for certain cases where there is discontinuity in the analog impulse response. A recommendation is to include a correction term in the digital filter. After that, the steady state bias in the digital filter is then suppressed. Moreover, the MATLAB R2021a command “impinvar” needs to also include a correction term so that the frequency and step responses can be more accurate in the digital filter. Two comparative studies were carried out to compare the improved IIF filter with three competing digital IIR filter design methods. Although the above issues and improvements have been proposed by researchers in the past, many researchers, engineers, and students are still not aware of them. This paper provides a fresh revisit of these issues and improvements by using figures, equations, and examples. Proper credits are also given to those researchers who first pointed out those issues and improvements. It is hoped that through an open access journal, future rediscovery of issues and improvements in IIF can be prevented.