Design Equations for Jointly Optimized Frequency-Response Masking Filters

A very efficient technique to drastically reduce the number of multipliers and adders in narrow transition-band linear-phase finite-impulse response digital filters is to use the one-stage or multistage frequency-response masking (FRM) approach, which has been originally introduced by Lim and further improved by Lim and Lian. In these original synthesis techniques, the subfilters in the overall implementation are separately designed. As shown earlier by the authors of this contribution together with Johansson, the arithmetic complexity in one-stage FRM filter designs can be considerably reduced by using the following two-step technique for simultaneously optimizing all the subfilters. First, a suboptimal solution is found by using a simple design scheme. Second, this solution is used as a start-up solution for further optimization, which is carried out with the aid of an efficient nonlinear optimization algorithm. This paper exploits this approach to synthesizing multistage FRM filters. An example taken from the literature illustrates that both the number of multipliers and the number of adders for the resulting optimized multistage FRM filters are approximately 70 percent compared with those of the filters synthesized using the original multistage FRM filter design schemes. Additional examples are included in order to show the benefits provided by the proposed synthesis scheme over other recently published design techniques, in terms of an improved performance of Some parts of this paper were presented at 158 Circuits Syst Signal Process (2011) 30: 157-183 the resulting solution, a higher accuracy of the solution, and a faster speed required to arrive at the best solution.

Section: Estimation Of the Design Parameters For The Proposed Synthesmentioning

confidence: 91%

“…Consider the following specifications [4,7,11,13,15,17,19]: ω p = 0.4π , ω s = 0.402π , δ p = 0.01, and δ s = 0.001. For the conventional direct-form FIR filter, the minimum order to meet the given criteria is 7 2558, requiring 1290 multipliers and 2558 adders when the coefficient symmetry is exploited.…”

Section: Filter Specificationsmentioning

confidence: 99%

An Efficient Algorithm for the Optimization of FIR Filters Synthesized Using the Multistage Frequency-Response Masking Approach

Yli‐Kaakinen

Saramäki

2010

“…However, in the case of a joint optimization of the constituent digital sub-filters, an empirical investigation led to α = 2.25 in [22], while an analytical investigation in [17] led to α = 2.4. In this paper, a better approximation for the interpolation factor M is obtained by tabulating the overall bandpass …”

Section: Design Of Bandpass Frm Fir Digital Filtersmentioning

confidence: 99%

“…Other gradient-based optimization techniques for FRM digital filters include the weighted least-squares approach [23] and the semi-definite [12] and second-order cone programming [13] approaches. Recently, a more attractive technique based on non-linear programming was developed [17] (see also [22]) for the joint optimization of the constituent digital sub-filters, leading to a substantial reduction in the number of addition and multiplication operations in the realization of the overall FRM digital filter. A further reduction was also possible by constructing the corresponding masking digital sub-filters in terms of a common part.…”

Section: Introductionmentioning

confidence: 99%

A Novel Diversity-Controlled Genetic Algorithm for Rapid Optimization of Bandpass FRM FIR Digital Filters Over CSD Multiplier Coefficient Space

Kilambi

Nowrouzian

2008

The conventional frequency response masking (FRM) approach is one of the most well-known techniques for the design of sharp transition band finite impulse response (FIR) digital filters. The resulting FRM digital filters permit efficient hardware implementations due to an inherently large number of zero-valued multiplier coefficients. The hardware complexity of these digital filters can further be reduced by representing the remaining (non-zero) multiplier coefficient values by using their canonical signed-digit (CSD) representations. This paper presents a novel diversitycontrolled (DC) genetic algorithm (GA) for the discrete optimization of bandpass FRM FIR digital filters over the CSD multiplier coefficient space. The resulting bandpass FIR digital filters are permitted to have equal or unequal lower and upper transition bandwidths. The proposed DCGA is based on an indexed look-up table of permissible CSD multiplier coefficients such that their indices form a closed set under the genetic operations of crossover and mutation. The salient advantage of DCGA over the conventional GA lies in the external control over population diversity and parent selection, giving rise to a rapid convergence to an optimal solution. The external control is achieved through the judicious choice of a pair of DCGA optimization parameters. An empirical investigation is undertaken for choosing appropriate values for these control parameters. The convergence speed advantages of the DCGA are demonstrated through its application to the design and optimization of a pair of bandpass FRM FIR digital filters with equal or arbitrary lower and upper transition 600 Circuits Syst Signal Process (2008) 27: 599-625 bandwidths. In both cases, an increase of about an order of magnitude in the speed of convergence is achieved as compared to the conventional GAs.

“…the filter structure, the design method, and the implementation. The introduction of various FRM structures has significantly enhanced the computational efficiency of the FRM technique [19,21,22,25,45,[48][49][50][51][52][53]. Non-linear optimization techniques further reduce the arithmetic operations in the FRM filters, where the coefficients of all subfilters in an FRM structure are optimized simultaneously [6, 15-18, 31, 34, 35].…”

mentioning

confidence: 99%

Frequency-Response Masking Filters Based on Serial Masking Schemes

Wei

Lian

2009

Self Cite

In this paper, computationally efficient filter structures based on the frequency-response masking (FRM) technique are proposed for the synthesis of arbitrary bandwidth sharp finite impulse response (FIR) filters. A serial masking scheme is introduced in the new structures to perform the masking task in two stages, which reduces the complexity of the masking filters. Compared to the original FRM and interpolated FIR-FRM (IFIR-FRM) structures, the proposed structures achieve additional savings in terms of numbers of arithmetic operations.