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.