Design and analysis of transient IIR filters with multiple frequency initialization using equivalent FIR filters

IIR filters designed for steady state operation suffer from the transient effect caused by processing a finite number of samples. Their performance, however, can be improved by using initialization techniques. This paper presents a new design method of IIR filters when processing a limited number of samples. An equivalent FIR filter for an IIR filter with multiple-frequency initializations is derived. This is then used in a design method that minimizes the mean squared-error between the steady state and the transient frequency responses. Filters designed using this method are shown to offer better transient frequency responses when compared to conventional steady state filters with and without initialization.