## Optimization of Frequency-Response-Masking Based FIR Filters

T. Saramäki, J. Yli-Kaakinen,
and H. Johansson
"Optimization
of frequency-response-masking based FIR filters,"
*J. Circuits Syst. Comput.*, vol. 12, no. 5,
pp. 563–591, Oct. 2003.

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Electronic version of an article published as
*Journal of Circuits, Systems, and Computers*,
vol. 12, no. 5, 2003, pp. 563–591 (doi: 10.1142/S0218126603001070)
© copyright World Scientific Publishing Company. http://www.worldscinet.com/jcsc/jcsc.shtml

### 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.Fig: An efficient implementation for a filter synthesized using the FRM approach. |
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Fig: Magnitude response for the best proposed overall filter with separate masking filters. |
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### BibTeX

`@Article{saramaJCSC03,`

author = {T. Saram{\"a}ki and J. Yli-Kaakinen and H. Johansson},

title = {Optimization of frequency-response-masking based
{FIR} filters},

journal = {J. Circuits Syst. Comput.},

year = 2003,

volume = 12,

number = 5,

pages = {563--591},

month = {Oct.}

}