Note on Generalized Linear-Phase Property of Discrete-Time Finite Impulse Response Systems

摘要

A discrete-time linear time-invariant system is said to have generalized linear phase if its frequency response takes the form: H(e~(jω)) = A(e~(jω)e~(-jαω+jβ), |ω| < π, where α and β are real constants and A(e~(jω) is real-valued. By a simple analyticity argument, we show that for finite impulse response systems to have generalized linear phase, the group delay α must be integer or half integer, a crucial step to complete characterization of such systems.