Frequency-domain considerations of LSV digital filters

The present paper develops a framework for the analysis and synthesis of linear shift-variant (LSV) digital filters in the frequency domain. First, LSV digital filters are theoretically modeled by the successive use of linear shift-invariant (LSI) filters. On the basis of the model, we present an interpretation of shift-variant spectral modification or filtering. Further, shift-variant digital filtering is discussed in relation to the notions of the short-time spectrum and the generalized frequency function. In addition, we propose an efficient implementation procedure which reduces the number of filter coefficients and the amount of computation. The effectiveness of LSV digital filters in processing time-varying signals is demonstrated by experimental verification.