Regular orthonormal and biorthogonal wavelet filters

Abstract

New methods for half-band filter design are developed, which structurally incorporate the regularity constraint into the design procedure. The first method results in half-band filters which do not have strictly positive frequency response. It is suitable for one class of biorthogonal filter banks. The second method results in half-band filters with strictly positive frequency response from which orthonormal wavelet filters can be obtained by spectral factorization. All filters are regular and have sharp transition bands. A new factorization of the first polyphase component of every half-band filter is found. This factorization suggests an efficient implementation of biorthogonal filter banks of the type considered. The implementation not only preserves the perfect-reconstruction property assuming finite word-length arithmetic, but has reduced coefficient sensitivity compared with the direct form. The properties of the resulting scaling functions and wavelets are summarized.