The authors have proposed a design method for two-dimensional (2-D) separable-denominator (SD) periodically time-variant digital filters (PTV DFs) and confirmed their superiority over 2-D time-invariant DFs. In that result, the periodicity matrix representing the periodicity of the varying filter coefficients is, however, restricted to two cases. This paper extends that idea so that the input-output relation of 2-D SD PTV DFs with an arbitrary periodicity matrix can be determined. This enables us to design wide range of 2-D PTV DFs.

This paper discusses a design method for two-dimensional (2-D) periodically time-variant digital filters (PTVDFs) whose filter coefficients vary periodically. First, 2-D periodicities for a variation of filter cefficients are considered, from which two and four-phase variations of coefficients are shown to be suitable for practical applications. Then, the input-output relation (transfer function) for 2-D separable-denominator (SD) PTV DFs is derived, which results in a linear combination of the baseband input signal and its modulated versions. Finally, in order ro approximate given filter specifications, the structure for 2-D SD PTV DFs is given and a design method is proposed. It is shown that, compared with the 2-D SD time-invariant DFs, approximation error can be reduced with the proposed SD PTV DFs.