A simple form synthesis of linear time-variant digital filter via spectral decomposition of its impulse response

Abstract

The paper describes a new technique to synthesize a finite impulse response of linear time-variant (LTV) digital filter. First, a finite impulse response is decomposed into a sum of products of two orthogonal sequences. The direct implementation of the decomposed impulse response leads to the parallel connection of linear time-invariant (LTI) digital filters, followed by time-varying multipliers. A simple filter structure is obtained by properly modifying the sequences to realize the parallel form structure as a cascade connection of first- or second-order recursive LTI filters. The structure is easy to implement on a computer and saves computation time. Numerical examples illustrating the technique are included.