Design and implementation of computationally efficient digital filters

Abstract

In this thesis, a weighted least square (WLS) design method is proposed for the parallel structure filters. Design equations are proposed to estimate the subfilter lengths in a basic parallel filter. A new set of design equations are developed for jointly optimized FRM filters. These equations give accurate estimations of subfilter lengths and the interpolation factor in a jointly optimized FRM filter. Problems are pointed out if the prototype in an FRM filter is even-length. New structures are proposed for the synthesis of FRM filters with even-length prototype filters. With the sequential quadratic programming technique, even-length prototype filters can further reduce the complexity of an FRM. A new design method is proposed to improve design efficiency of jointly optimized FRM filters. This method is based on a dynamic frequency grid point allocation scheme, and saves memory and computing time significantly.