Comparative Analysis of Shift Variance and Cyclostationarity in Multirate Filter Banks

Multirate filter banks introduce periodic time-varying phenomena into their subband signals. The nature of these effects depends on whether the signals are regarded as deterministic or as random signals. We analyze the behavior of deterministic and wide-sense stationary (WSS) random signals in multirate filter banks in a comparative manner. While aliasing in the decimation stage causes subband energy spectra of deterministic signals to become shift-variant, imaging in the interpolation stage causes WSS random signals to become WS cyclostationary (WSCS). We provide criteria to quantify both shift variance and cyclic nonstationarity. For shift variance, these criteria separately assess the shift dependence of energy and of energy spectra. Similarly for nonstationarity, they separately assess the nonstationary behavior of signal power and of power spectra. We show that, under aliasing cancellation and perfect reconstruction constraints of paraunitary and biorthogonal filter banks, these criteria evaluate the behavior of deterministic and WSS random signals in a consistent, dual way. We apply our criteria to paraunitary and biorthogonal filter banks as well as to orthogonal block transforms, and show that, for critical signals such as lines or edges in image data, the biorthogonal $9/7$ filters perform best among these.