TIME-VARYING BIORTHOGONAL FILTER BANKS - A STATE-SPACE APPROACH

Using state-space representations of biorthogonal time-varying filter banks, it is possible to come up with a theory for the transitional be havior between two stationary filter banks, The transition interval de pends on the size of the common subspace spanned by the controllabilit y operators of the initial and final filters on the decomposition side s, and the common subspace spanned by the observability operators of t he filters on the reconstruction sides, When the respective operators span the same spaces, we can derive conditions under which the transit ion between the filter banks can be so controlled that both the decomp osition and the reconstruction functions gently embrace, For such filt ers, the transition interval can be made arbitrarily short, If it is z ero, then the special case of instantaneous transition is reached.