Analysis and synthesis of linear shift-variant digital filters

A framework for the analysis and synthesis of linear shift-variant (LSV) digital filters in both time and frequency domains is developed. The interrelaionships among the impulse response, the shift-variant difference equation and the generalized transfer function of an LSV digital filter were investigated. The necessary and sufficient conditions for realizing an impulse response and a rational generalized transfer function as recursive shift-variant difference equations are derived. An LSV digital filter is applied to modify the short-time spectrum of a nonstationary sequence. It is shown that the shift-variant hort-time spectral modification can be implemented using a nonrecursive LSV digital filter, providing a frequency-domain interpretation of shift-variant filtering process. Problems associated with the synthesis and implementation of recursive LSV digital filters are investigated.