REGULAR ORTHONORMAL AND BIORTHOGONAL WAVELET FILTERS

New methods for half-band filter design are developed, which structura lly incorporate the regularity constraint into the design procedure. T he first method results in half-band filters which do not have strictl y positive frequency response. It is suitable for one class of biortho gonal filter banks. The second method results in half-band filters wit h strictly positive frequency response from which orthonormal wavelet filters can be obtained by spectral factorization. All filters are reg ular and have sharp transition bands. A new factorization of the first polyphase component of every half-band filter is found. This factoriz ation suggests an efficient implementation of biorthogonal filter bank s of the type considered. The implementation not only preserves the pe rfect-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 su mmarized. (C) 1997 Elsevier Science B.V.