Overflow Oscillations in Digital Filters

A digital filter using idealized operations can easily be designed to be stable. 1 Nevertheless, in actual implementations, the output of such a stable filter can display large oscillations even when no input is present.* A known cause of this phenomenon is the fact that the digital filter realization of the required addition operation can cause overflow, thereby creating a severe nonlinearity. f Our purpose here is twofold. The first is to give a somewhat detailed analysis of the character of the oscillations when the filter is a simple second order recursive section with two feedback taps. This unit is the fundamental building block for the cascade and the parallel realization of digital filters, and as such is worthy of some scrutiny. 2 A simple conclusion which one can draw from * To the best of our knowledge, these oscillations were first observed and diagnosed by L. B. Jackson of Bell Telephone Laboratories. t In the present work rounding errors in multiplication or storage are neglected and therefore so are the little-understood oscillations attendant upon these nonlinearities. 2999