A SUFFICIENCY CRITERIA FOR ORTHOGONAL QMF FILTERS TO ENSURE SMOOTH WAVELET DECOMPOSITIONS

For the case of orthogonal QMF filters with maximum vanishing moments (MVM), there are only a finite number of N-point FIR filters that sati sfy the constraint set, and all those solutions that are known result in continuous decompositions (N greater than or equal to 4). Unfortuna tely, there are solutions to the non-maximum vanishing moment problem that result in wavelet decompositions that are highly irregular (i.e., discontinuous). This paper introduces a simple inequality constraint that can be used to quickly assure continuous wavelet decompositions f or a non-maximum vanishing moments (non-MVM) solution. This is useful in schemes where the QMF filter is dynamically chosen (e.g., signal de pendent compression). The sufficiency requirement developed is much ea sier to implement than the constraint on the Fourier transform of the filter developed previously. In addition, it can be easily extended to stricter regularity requirements (e.g., filters that are both continu ous and differentiable). (C) 1995 Academic Press, Inc.