Optimization of Frequency-Response Masking Based Fir Filters

Abstract

A very efficient technique to drastically reduce the number of multipliers and adders in implementing linear-phase finite-impulse response (FIR) digital filters in applications demanding a narrow transition band is to use the frequency-response masking (FRM) approach originally introduced by Lim. The arithmetic complexity can be even further reduced using a common filter part for constructing the masking filters originally proposed by Lim and Lian. A drawback in the above-mentioned original FRM synthesis techniques is that the subfilters in the overall implementations are separately designed. In order to further reduce the arithmetic complexity in these two FRM approaches, the following two-step optimization technique is proposed for simultaneously optimizing the subfilters. At the first step, a good suboptimal solution is found by using a simple iterative algorithm. At the second step, this solution is then used as a start-up solution for further optimization being carried out by using an efficient unconstrained nonlinear optimization algorithm. An example taken from the literature illustrates that both the number of multipliers and the number of adders for the resulting optimized filter are less than 80% compared with those of the FRM filter obtained using the original FRM design schemes in the case where the masking filters are separately implemented. If a common filter part is used for realizing the masking filters, then an additional reduction of more than 10% is achieved compared with the optimized design with separately implemented masking filters.

Techniques for Efficient Implementation of FIR and Particle Filtering

“…Typically, each of the sub-filter is designed by optimization separately. A significant reduction in the implementation cost can be achieved by simultaneously optimizing the sub-filters together [20]. Joint optimization has been applied to both the original FRM [48] and the generalized FRM [260].…”

Design Equations for Jointly Optimized Frequency-Response Masking Filters

“…It is clear from examples in [26], [27], [31], [33], [34], [38] that the transition bandwidths are almost the same for two masking filters. However, their lengths are not the same.…”

“…For design example VII [20], the best design requires 91 coefficients, i.e., N a = 45, N Ma = 19, N Mc = 27, with an interpolation factor of 9 calculated using (15). For the interpolation factors of 7 and 8 estimated by (1) and (2) It is worth noting that the proposed design equations are applicable to FRM filters synthesized with other nonlinear optimization techniques [26]- [28], [31], [33], [34], [38] although they are derived based on the FRM filters designed by the SQP technique. The reason is that the use of nonlinear optimization techniques is intended to produce a globally optimized design, e.g., a filter with a minimum number of coefficients satisfying the given specifications.…”

“…Much research effort has been made to improve the computational efficiency of FRM filters in recent years. A notable effort is to employ nonlinear optimization techniques to jointly optimize all subfilters in an FRM structure [26]- [28], [31], [33], [34], [38]. Such an approach leads to about 20% additional savings in terms of number of multipliers.…”

A Generalized Oversampled Structure for Cosine-Modulated Transmultiplexers and Filter Banks

“…In addition, one may combine the channel split-and-add method with the frequency-response masking (FRM) approach [7], [8], including its optimized versions [9], [13], giving more flexibility on the choice of the interpolation factor for the FRM-based filter, as illustrated in [2].…”