Zero-pinning the Bernstein polynomial: a simple design technique for orthonormal wavelets

Abstract

A novel technique is presented for designing finite impulse response orthonormal wavelet filters. The filters are obtained from the spectral factorization of an appropriately designed parametric Bernstein polynomial. We show that by strategically "pinning" some of the zeros of the polynomial, the nonnegativity requirement on the polynomial, which is mandatory for orthonormal filter design, can be easily achieved. Filters with a high number of vanishing moments and sharper frequency response (but lower vanishing moments) than the maximally flat Daubechies filters can be easily designed. The technique is simple as it only involves solving linear equations yet is versatile as filters with different characteristics can be obtained with ease.