An alternating variable approach to FIR filter design with power-of-two coefficients using the frequency-response masking technique

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.…”

“…In another class of joint optimization techniques, the subfilters are optimized alternately [1, 8-10, 32, 37]. We call them alternating variable approaches, the name of which firstly appeared in [9]. The method in [9] focuses on the FRM filter design with power-of-two coefficients, where the subfilters are improved iteratively by fixing the others and the optimization of a subfilter is done via a branch and bound method over a subregion of the search space.…”

“…We call them alternating variable approaches, the name of which firstly appeared in [9]. The method in [9] focuses on the FRM filter design with power-of-two coefficients, where the subfilters are improved iteratively by fixing the others and the optimization of a subfilter is done via a branch and bound method over a subregion of the search space. In [32,37], the methods proposed by Saramäki et al first find an initial FRM filter by alternately optimizing the subfilters and then further optimize these obtained subfilters simultaneously using a nonlinear optimization technique.…”