Time-varying filter banks and multiwavelets

Abstract

A wavelet construction by Geronimo, Hardin and Massopust uses more than one wavelet and scaling function. Strang and Strela gave a filter bank interpretation of that result, as well as a condition for moment properties of the resulting wavelets. The present authors are concerned with the regularity of the resulting iterated filter bank scheme, that is, a matrix extension of the classic result by Daubechies (1988) on iterated filters. They show in particular: (i) the relation between time-varying filter banks and multiwavelets, (ii) the construction of multiwavelets as limits of iterated time-varying filter banks, (iii) a necessary condition for the convergence of the iterated matrix product and (iv) an exploration of examples of multiwavelets as iterations of time-varying filter banks.<>