Quantitative Comparison of Shift Variance and Cyclostationarity in Multirate Filter Banks

We analyze the behaviour of deterministic and wide-sense (WS) stationary random signals in multirate filter bank branches. We focus on subband energy spectra and energies for deterministic signals, and on subband power spectra and powers for random signals. We show that energy spectra and power spectra behave funda-mentally different in a filter bank branch: aliasing in decimation causes energy spectra and energies of deter-ministic signals to be translation variant. The shapes of power spectra of WS stationary random signals are also affected by decimation, but signals remain WS sta-tionary. Interpolation by upsampling and anti-imaging filtering attenuates the translation-variant effects. WS stationary random signals, however, generally become WS cyclostationary during interpolation unless a per-fectly bandlimiting anti-imaging filter is used. Transla-tion variance of deterministic signals hence originates from non-ideal analysis (anti-aliasing) filtering, while WS-cyclostationarity of random signals originates from non-ideal synthesis (anti-imaging) filtering. We describe translation variance and cyclostationarity in terms of the filter bank parameters in a comparative manner, provide measures to quantify translation variance and cyclostationarity, and briefly address the consequences of perfect reconstruction constraints.