Optimal Design Of FRM Filters And Two-dimensional Filters

The frequency-response-masking(FRM) approach is one of the mostefficient technique to synthesize linear-phase finite-impulse response(FIR)digital filters with sharp transition bands. This approach drastically reducesthe complexity of filters by producing filters with very sparse coefficientscompared with conventional direct design methods.Since Y.C.Lim's presented the frequency-response-masking technique forthe design of finite-impulse response digital filters with very sharptransition widths in 1986, the analysis and optimal design of FRM filtershas been a study subject for researchers. They proposed several differentmodified approach on FRM filter structure and optimal design algorithm,respectively, in order to reduce the filter complexiy even further. This paperproposed a new approach for design of efficient sharp finite-impulseresponse digital filters by utilizing the frequency-response-maskingtechnique based on a neural-networks optimal design algorithm. The mainidea is to minimize the squared-error function in the frequency-domain toobtain FRM filter coefficients. In this paper, we firstly introduce thefundamental principle and several existing optimal design approach of FRMtechnique, then algorithmic details for the design of FRM filter based onneural-networks were presented, the stability theorem was also proved toillustrate the validity of the proposed algorithm, and the implementation ofthe approach was described together with some design guidelines. Somesimulations were included and the results show that the proposed algorithmcan design better FRM filters than conventional methods.During the last three decades ,two-demensional(2-D) filters design hasreceived growing attention by researchers working in image processing,seismic data processing, X-rays enhancement, astronomy, etc. Bothfinite-impulse response(FIR) and infinite-impulse response(IIR) 2-D filtershave been studied extensively. Since FIR filters can easily be made to havelinear-phase and are inherently stable, they are often preferred over IIRfilters, especially in applications where the linear-phase of the signal is tobe preserved.A batch back-propagation neural networks approach was presented to design general 2-D quasi-equripple linear-phase finite-impulse responsedigital filters. By minimizing the frequency-domain weighted error function,the filter coefficients was obtained. Algorithm details and stability based onthe neural-networks were presented. Several design examples were alsogiven and the results show that the neural netwrok method can easilyachieve higher design accuracy than some conventional methods.