First Order Digital Filters—An Audio Cookbook

The simplest digital filters are first order FIR and IIR filters, singly or in cascade. While not as powerful as higher order filters, they are nevertheless of considerable interest in audio for bass and treble controls, DC offset removal, high pass filters, and low pass filters. Also appealing is the low computational burden that first order filters place on DSP resources.

Despite the simplicity of the first order filter, the DSP literature is not forthcoming with a simple methodology that allows for cookbook design. The method presented here appears in an article from 1978 by Ham and is based on relating a prototype analog filter to the desired digital filter using the technique of impulse invariance.