Analysis of digital IIR filters processing finite numbers of samples with single frequency initialisation

This paper deals with new analysis techniques for digital IIR filters operating in the transient mode and utilising single frequency initialisation. Single frequency initialisation forces the transient response of the digital filter to reach its steady state at a particular frequency irrespective of the number of processed samples. These techniques are based on deriving an equivalent FIR filter for the IIR type and its associated initialisation processor. The analysis which covers both zero and non-zero frequency initialisation includes the transient frequency responses, bandwidth and stop-band characteristics