Design Of Recursive Digital Filters In View Of Their Robustness

In this paper, some issues of the design of recursive digital filters in view of their robustness are discussed. After giving some general remarks regarding the mechanisms of arising nonlinear distortion in filters, and regarding the robustness property, two problems are considered in detail. That is the forced-response stability and occurrence of harmonic distortion, are investigated. It is shown here that the forced-response stability is equivalent to the attractivity property of the (realized) filter. Furthermore, the harmonic distortion due to the finite wordlength in a class of digital filters of which poles lie near the point z = 1 is analysed, too. It is shown that by applying the method of harmonics balance it is possible to obtain the closed-form results for the higher harmonics and for the change in the filter transfer function. The expressions obtained describe, however, only qualitatively the phenomenon discussed; they do not provide quantitative results