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

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Abstract

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 the resulting solution, a higher accuracy of the solution, and a faster speed required to arrive at the best solution.

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Authors and Affiliations

  1. Department of Signal Processing, Tampere University of Technology, P.O. Box 553, 33101, Tampere, Finland

    Juha Yli-Kaakinen & Tapio Saramäki

Authors
  1. Juha Yli-Kaakinen
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  2. Tapio Saramäki
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Correspondence to Juha Yli-Kaakinen.

Additional information

Some parts of this paper were presented at the 2002 IEEE International Conference on Electronics, Circuits and Systems, Dubrovnik, Croatia, September 2002. This work was supported by the Academy of Finland, project No. 44876 (Finnish Centre of Excellence Program (2000–2005)). Juha Yli-Kaakinen was also financed by a postdoctoral research grants from the Academy of Finland, project Nos. 75492 and 105823.

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Yli-Kaakinen, J., Saramäki, T. An Efficient Algorithm for the Optimization of FIR Filters Synthesized Using the Multistage Frequency-Response Masking Approach. Circuits Syst Signal Process 30, 157–183 (2011). https://doi.org/10.1007/s00034-010-9216-2

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  • DOI: https://doi.org/10.1007/s00034-010-9216-2

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