Shift Variance and Cyclostationarity in Multirate Filter Banks

Multirate filtering generally introduces time-varying phenomena into the decomposed signals. These phenomena depend on whether the signals are viewed as deterministic, or as wide-sense (WS) stationary random signals. We consider the behaviour of subband energy spectra and subband energies for deterministic signals, and of subband power spectra and subband power for WS stationary random signals. We show that aliasing in decimation causes energy spectra and energies of deterministic signals to be translation variant, but leaves WS stationary random signals WS stationary. Interpolation by upsampling and anti-imaging filtering attenuates translation variance of deterministic signals, but converts WS stationary random signals into WS cyclostationary random signals. In perfect reconstruction (PR) filter banks, the time-varying effects of the filter bank channels cancel out. Subband signal processing such as filtering or quantization, however, distorts the balance between the filter channels and lets these effects appear in the output signal. Based on our analysis, we therefore derive quantitative measures for translation variance and cyclostationarity. These may be used to compare different multiratefilter banks.