Design of FIR Filte using Filte Response Masking Technique Sandeep Shivastava, Alok Jain, Ram Kuma Soni Abstact- In this pape autho is tying to implement Fequency esponse masking (FRM) technique. In this technique the fequency esponses of complementay pai filtes ae masked by the fequency esponses of two appopiate masking filtes. These masking filtes can be designed with method of FIR filte designing; window technique is used hee fo the same pupose. Keywods: FRM I. Intoduction Fequency esponse masking technique is fist intoduced by Yong ching Lim in 1986 [1]. It was a simplest implementation technique whee M delay intoduced to linea phase low-pass filte esultant bette steepe tansition fom pass-band to stop-band. FRM technique is futhe optimized in one and two dimensional FIR filte designing by Y C Lim and Yong Lian in 1993 [2][3]. This pape is oganized as section I is about the intoduction and histoy of FRM technique and basic aspects of it. Section II, III and IV ae about implementation of FRM technique in stage-i, stage-ii and stage-iii. Final conclusion is made in section-v. II. FRM Stage-I Initially two linea phase Finite impulse esponse filtes and is consideed which complement with each othe. Fequency esponse of the filtes is defined as (1) Whee N is length of the filte and is a tigonomety function given below in equation (2) and fig. (1): (2) The fequency esponse of complementay filte is (3) θ Figue 1 Tigonomety function O it can be also epesented as 211 Sandeep Shivastava, Alok Jain, Ram Kuma Soni (4)
Which means can be calculated by subtacting with delay function shown in fig. (2); Whee will be consideed as any input function applied into it and Conside low pass FIR filte designed using window technique having cut-off fequency θ. Because of the complementay pai of and it will be epesented as (5) Figue 2 filte with delay function Now, afte analyzing the basic stuctue of the FIR filtes; block diagam of fist stage of implementation of FRM technique is shown in fig. (3). Figue 3 Stuctue of fequency esponse masking technique Two filtes and ae fomed by including delay of in fequency esponse of given filtes and. Theefoe and. Two masking filtes and ae also consideed to mask fequency esponse of the given filtes and. Implementation of masking filte will be done by window technique of FIR filte design. Hee hamming window is used fo implementation of masking filte. The complete stuctue is as shown in flow chat ( Appendix A). The geneated esponse of fist stage filte and analysis synthesis side is as shown in figue 4 and figue 5 espectively. 212 Sandeep Shivastava, Alok Jain, Ram Kuma Soni Figue4 fist stage FRM output (db)
Figue5 Analysis and synthesis esponse of the fist stage of FRM III. FRM Stage-II Conside fo the implementation of second stage FRM filte that and ae the pass-band and stop-band fequencies. Complementay filte will also be calculated fo second stage FRM filte epesented by (6) 1 st condition: Let us consideed and ae pass-band and stop-band fequencies fom the fist stage FRM filte i.e. and Pass-band and stop-band fequencies again calculated fo the second stage masking filtes and. These ae epesented as,,, pass-band and stop-band fequencies of and espectively. Now, the elation between these given fequencies and expessed below- & (7) IV: FRM Stage-III Fo the thid stage of implementation pass-band and stop-band fequencies ae consideed as and. As pe the condition of thid stage complementay filte will be calculated as 213 Sandeep Shivastava, Alok Jain, Ram Kuma Soni (9)
Figue6 second stage of FRM Table1: Second stage FRM fequency ange Fequency ange 1 Stage II Condition 1 Condition 2 Fequency ange 2 Fequency ange 3 Pat1 Pat2 2nd condition: Similaly fo second condition,,, ae the pass-band and stop-band fequencies of and espectively. So, elation with to the fequencies given below- & (8) The above equation (7) and (8) helps to calculate the cutoff fequencies of second stage shown in table (1). Thee is final fequencies and fom the second stage that will be conside as input fo thid stage as and i.e. ( and ). Simila to pevious stage implementation hee also two conditions will be consideed- 1 st condition: and consideed as masking filtes of thid stage having pass-band and stop-band fequency,,, espectively. The condition of input will be consideed as and. Now, the elation between these given fequencies and expessed. 214 Sandeep Shivastava, Alok Jain, Ram Kuma Soni
2nd condition: Fo the second condition of thid stage,,, ae the pass-band and stop-band fequencies of and espectively. So, elation with to the fequencies given as shown in table (2) Figue 5: Block diagam of thid stage FRM filte V. VI. Conclusion Fom the calculation of these thee stages it has been clea that as the stages ae inceasing the expected cutoff of the filte will become shape, but complexity of the stuctue inceases with stages. The ate of iteation will also make the speed slowe. This method of designing can be utilized to optimize the OFDM paametes like ISI and ICI. It will give the scope of aea to the eseaches. Table3 Thid stage of FRM fequency ange Fequency ange 1 Stage III Condition 1 Condition 2 Fequency ange 2 Pat1 Fequency ange 3 Pat2 215 Sandeep Shivastava, Alok Jain, Ram Kuma Soni
Appendix A Whee, ( ) ( )} Replacing Delay of and by M delay Masking Filte Masking Filte Addition Addition N=1,Stage II N=2 StageIII Pass band feq. = Max. Passband ipple = Stop band feq = Min stopband attenuation = 40dB Θ = 1.884 and ϕ = 1.9154 216 Sandeep Shivastava, Alok Jain, Ram Kuma Soni
Refeence: [1] Y.C. Lin Fequency esponse masking appoach fo the synthesis of shap linea phase digital filte. IEEE Tans. Cicuits Syst. Vol. CAS-33, pp 357-364, Ap 1986. [2] Y.C. Lin, Yong Lian The optimum design of one and two dimensional FIR filtes using the fequency esponse masking technique. IEEE Tans. Cicuits Syst. Vol. 40,No. 2 pp 88-95, Febuay 1993. [3] L R Rabine and B. Gold Theoy and application of design signal pocessing Englewood cliffs,pintice-hall,1975. (1) Sandeep Shivastava was bon in india, in 1982. He eceived his B.E. degee (honos) in Electonics & Communication Engineeing fom Pt. Ravishanka Univesity, Raipu, in 2004, and M.Tech. degee (honos) in VLSI Design fom RGPV, Bhopal. He was woked as Lectue in Electonics & Communication Depatment, LNCT, Bhopal. Cuently he is woking as Asst. Pofesso. In Electonics & Communication Depatment SIRT Bhopal and Ph.D. Schola in Samat Ashok Technological Institute Vidisha. (2) D. Alok jain was bon in India, in 1966. He eceived the B.E. degee in Electonics & Instumentation Engineeing fom Samat Ashok Technological Institute, Vidisha, India in 1988 and M.Tech. in Compute Science & Technology fom IIT, Rookee, India duing 1992. He eceived the Ph.D. degee in Electonics &CommunicationEngineeing fom Thapa Institute of Engineeing & Technology, Patiala, India in 2006. He is Pofesso, Depatment of Electonics & Instumentation, SATI, Vidisha. He is the membe of editoial advisoy boad of jounal titled, Recent Patents on Electical Engineeing, Bentham Science Publishe. He was the shot tem eseach fellow, IISc, Bangloe. His eseach aea is Signal pocessing, Soft computing and Powe Electonics. (3) D. R.K.Soni was bon in India, in 1966. He eceived his B.E.degee in Electonics &Instumentation fom Samat AshokTechnology Institute, Vidisha, in 1988, and M.Tech. degee in digital Communication fom Bhopal Univesity. He obtained his Ph.D.Degee fom RGPV Bhopal.He joined as a lectue in Samat Ashok Technology Institute (Polytechnic), Vidisha. Pesently, he is woking as Pincipal, Samat Ashok Technology Institute (Polytechnic), Vidisha. He has published about 10 papes in jounals and confeence poceedings. His cuent eseach inteest includes digital signal pocessing,filte banks, mobile communication and micopocesso andapplication. He eviewed eseach papes fo intenational confeences and jounals. 217 Sandeep Shivastava, Alok Jain, Ram Kuma Soni