A comparative study of some recursive digital filter design techniques
Warmack, Ralph E
Master of Science
This study explores four techniques for simulating analog filters by recursive digital filters. A uniform basis for comparing these methods is provided by requiring each digital filter to maintain the D.C. gain and order of the given analog filter. Three of these techniques are modified versions of existing methods found in the literature. The fourth is a proposed compensation scheme for the bilinear transformation which preserves the finite critical frequency locations of the original analog filter. For band-limited filters and for sampling intervals approaching zero, it is demonstrated that the D.C. gain requirement with the standard Z-transformation of the analog filter transfer function results in the so-called impulse-invariant method. The nature of the mappings induced by the bilinear transformation is investigated and some contours generated by this mapping are given. While under the most general conditions, none of these methods minimizes the mean-squared error at the sampling instants, it is shown that the frequency responses of these digital filters (in the Nyquist interval) and their unit-step responses are often acceptable approximations to those of the given analog filter and warrant their use as simulators. Some numerical examples are given which illustrate implementation of these filters. Roundoff accumulation errors are encountered and bounds which show the effect of filter order and sampling rate are discussed.