Design of halfband filters for orthonormal wavelets using ripple-pinning

The design of halfband filters for orthonormal wavelet with a prescribed number of vanishing moment and prescribed ripple amplitudes is described. The technique is an extension of the zero-pinning (ZP) technique and is called ripple-pinning (RP). In ZP, the positions of stopband minima (of a Bernstein polynomial) are specified explicitly and the stopband maxima (position and amplitude) depend implicitly on the minima. In RP, the amplitude of the ripples is explicitly specified and this leads to a set of non-linear (polynomial) equations with the position of both the minima and maxima as unknowns. An iterative algorithm is proposed to solve the equations and design examples will be presented. Two variations of the RP technique, which allow for the transition band sharpness to be explicitly specified, are also presented.