A weighted least squares approach to the design of FIR filters synthesized using the modified frequency response masking structure

Abstract

Abstract-This paper presents an application of the weighted least squares (WLS) method to the design of sharp linear phase finite-impulse response (FIR) digital filters synthesized using a modified frequency-response masking (FRM) structure. In our approach, the original minimax design problem is converted into a WLS problem. The WLS problem is highly nonlinear with respect to the coefficients of the filter. However, it can be decomposed into four linear least squares (LS) problems, each of which can be solved analytically. The design problem is then solved iteratively by using an alternating variable approach. The effectiveness of the method is demonstrated through solving a low-pass linear phase sharp FIR digital filter example.Index Terms-Frequency-response masking (FRM), minimax error, weighted least squares (WLS), alternating variable approach.

An Alternating Variable Technique for the Constrained Minimax Design of Frequency-Response-Masking Filters

“…Narrow transition band finite impulse response (FIR) digital filters have found many applications in digital signal processing, such as wireless communication systems, multimedia systems, and so on [3,4,16,22]. One of the most efficient approaches to synthesizing narrow transition band filters is the frequencyresponse-masking (FRM) technique, which was originally proposed by Lim in [17] and then improved by many researchers, e.g., Lim and Lian in [11,13,18,19], Lee et al in [8][9][10], Saramäki et al in [29][30][31][32]37] and Lu et al in [24][25][26]. The FRM technique produces filters with very sparse coefficients that require fewer number of multipliers and adders in their implementation than those yielded by the conventional direct design methods.…”

“…On the other hand, many researchers have developed design methods that optimize the subfilters jointly [1,[8][9][10][24][25][26]32,33,[37][38][39]. In most of these methods, all the subfilter coefficients are treated as a whole design vector and optimized simultaneously.…”

Neural Network Algorithm for Designing FIR Filters Utilizing Frequency-Response Masking Technique

“…This produces only suboptimal solutions, thereby very likely to lead to poor overall solutions. Recently, several joint optimization methods have been developed (see [9][10][11][12][13][14][15][16]). In [9][10][11][12], two genetic algorithms, a second-order cone programming approach and a two-step optimization technique are introduced, respectively.…”

“…However, a problem with the method is the large number of constraints that inevitably affect design efficiency and, in the case of highorder FRM filters, may cause numerical difficulties. In [14][15][16], a weighted least squares (WLS) method is used for designing linear-phase FRM filters. In [14], the original least squares (LS) problem is decomposed into two linear LS problems when designing basic structure of FRM filters.…”

“…In [14], the original least squares (LS) problem is decomposed into two linear LS problems when designing basic structure of FRM filters. In [15], the original LS problem is decomposed into four linear LS problems. In [16], the WLS method was used for designing multistage FRM filters.…”