A new approach for the analysis of a periodically time-varying recursive digital filter

A periodically time-varying (PTV) recursive digital filter is analyzed by an approach using the generalized transfer function of a PTV filter. As a result of the analysis, it is concluded that the generalized transfer function (GTF) of a PTV infinite impulse response (IIR) filter is determined uniquely by a given difference equation. The authors describe in detail how to obtain the GTF of a PTV filter from a given difference equation. The input and output relationship of a PTV recursive filter is derived by using its GTF. Several properties of a PTV recursive filter which cannot be obtained by the conventional analysis method are derived. One important property of a PTV IIR filter is that change of the cascade ordering in an equivalent structure of a PTV IIR filter does not affect its output. It is shown that the equivalent structure of a PTV recursive filter can be derived easily with the proposed method. It is concluded that the proposed approach is much more effective than the conventional analysis method for analyzing a PTV recursive filter