Least Squares Design of Orthonormal Wavelets via the Zero-Pinning Technique

A simple yet versatile technique was recently introduced for designing FIR orthonormal wavelet filters. The technique involves pinning some of the zeros of the parametric Bernstein polynomial to ensure non-negativity of the frequency response. 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 position of the pinned zeros can be easily adjusted to give a variety of frequency response. This paper extends the previous work and presents a method to determine the zeros´ position that will give a least squares error in the stopband response