PIECEWISE STATIONARY PERFECT RECONSTRUCTION FILTER BANKS

The problem that is addressed in this paper is whether there can be es tablished instantaneous transitions between stationary filter banks an d if so, what the conditions are under which such transitions are poss ible. It is shown that a perfect reconstruction stationary filter bank can be replaced - say at time instant n - with another constant filte r bank without violating the perfect reconstruction property at any ti me and with steady-state behavior of the replacement bank from time in stant n on, if the filters of the two analysis banks are proportionall y related and the impulse responses of the synthesis bank are inversel y proportionally related. Stated in another way, the time varying filt er bank should have a stationary state behavior over all time. The res ults are presented in terms of input-output maps as well as in terms o f realizations. Examples in both frameworks are also given, namely tra nsforms in the one and filter banks in the other.