IJSRD - International Journal for Scientific Reearch & Development Vol. 3, Iue 11, 2016 ISSN (online): 2321-0613 Deign and Analyi of IIR Peak & Notch Ravi Choudhary 1 Pankaj Rai 2 1 M.Tech. Student 2 Aociate Profeor 1,2 Department of Electrical Engineering 1,2 B.I.T Sindri Abtract The deign and analyi of infinite impule repone (IIR) peak and notch filter ha been performed, which i employed variou communication ytem to eliminate unwanted narrow band interference. In communication ytem, radio frequency band for FM lie between 88MHZ - 108MHZ. A method for deign of digital peak and notch filter of center frequency 90MHZ ha been preented. Two parametric value like pa band ripple & top band attenuation have been calculated by uing mathematical modelling. Variou tranpoed econd order ytem (SOS) algorithm uch a direct form I and II elliptic deign method have been applied. By tuning quality (Q)- factor, peak filter (order 4) and notch filter (order 2) for range of Q between 2-18 and 2 100000 repectively have been generated with the help of different RF & AF ocillator. approximation and order of the notch and peak filter determine overall performance in term of multiplier, adder, no. of tate, multi per input ample (MPIS) and add per input Sample (APIS) narrow band interference. From the realization perpective, the filter conume more power and become more complex with increae in filter order. It i eay to implement in communication at tranmitter or receiver point and ha good communication ytem repone. The oberved ettling time & fixed bandwidth gain confirm the performance of deigned filter. Key word: Notch, Peak, Adder, Multiplier, Quality Factor, RF & AF-Radio & Audio Frequency, APASS- Paband Ripple, ASTOP-Stopband Attenuation I. INTRODUCTION Digital filter play an important role in digital ignal proceing and communication ytem. A coniderable number of deign algorithm have been propoed for finiteduration impule repone (FIR) digital filter and (IIR) infinite-duration which are analog circuit to perform ignal proceing function. Thee paper preent performance analyi of Peak filter which i a type of band add filter to allow ingle frequency conidering the effect of noie. An ideal peak filter i a linear filter whoe frequency repone i characterized by a unity gain at all frequencie except at a particular frequency called the peak filter it gain i zero. Notch filter i able to remove narrowband or ingle frequency inuoidal interference while leaving broadband ignal unchanged. approximation and order of the Notch filter determine overall performance improvement in preence of narrowband interference. II. LITERATURE SURVEY The filter perform a election of the partial according to the frequencie that we want to reject, retain or emphaize. i a linear tranformation. A an extenion, linear tranformation can be aid to be filter. The vocal cord produce a ignal with a fixed harmonic pec- trump wherea the cavitie act a acoutic filter to enhance ome portion of the pectrum [1]. The digital fixed notch and peak filter which are rated baed on value of their q-factor. Generally, the higher the Q-factor, the more exact the notch and peak filter. A notch and peak filter with a low Q-factor may effectively notch and peak out a range of frequencie, wherea a high Q factor filter will only delete the frequency of interet [2]. Fixed notch and peak filter i deigned to remove a ingle fixed noie preent at ingle frequency in communication ytem which i either at tranmitter or at receiver.the deign of a filter tart with pecifying the deired two baic parameter (APASS AND ASTOP) have to be determined[3].we know in communication ytem for example frequency of FM lie between (88MHZ-108MHZ) and our frequency of interet i to remove noie exiting at 90MHZ.To achieve thi we keep the frequency contraint factor like center frequency or fixed notch frequency at 90 MHz and fix order of the ytem to be 2nd. we elect direct form l and II order ection a our filter tructure becaue it ue le number of delay element and elliptic deign algorithm [4]. Amandeep kaurmaan et. al. worked on the performance of Notch and Peak filter of order 2 and 4 repectively have been analyed for different value of Q- factor we change another frequency contraint factor like quality factor notch filter from (2-100000) and peak filter from (2-18).There i variation in output gain of notch and peak filter from (25.0663-16029.0728),(1.05930-102249) and fixed bandwidth gain to be - 3.0103db for every value of Q factor[5]. C. Charoenlarpnopparut et. al. ha been done we check all the repone for different value of quality and the performance of notch filter that wort repone i oberved at Q=2 and bet repone i oberved at Q=90000 and peak filter performance of that wort repone i oberved at Q=2 and bet repone i oberved at Q=16. We find the ettling time to be 13.8 nec and fbw 20db to be 9045.3 khz. The 20 db bandwidth i an indication of the attenuation. For minimum ettling time the filter order hould be a low a poible. From the realization perpective, the filter conume more power and become more complex with increaing filter order due to the growing number of multiplier, adder and delay element [6].Therefore thi paper preent dicuion of digital fixed notch and peak filter which are rated baed on bai of their Q-factor. III. DETERMINATION OF APASS AND ASTOP-BY MATHEMATICAL EQUATION FOR PEAK AND NOTCH FILTER Two parametric value like (APASS & ASTOP) have been calculated by uing mathematical modelling for a given order, we can obtain harper tranition by allowing for Apa band ripple and/or Atop band attenuation. All right reerved by www.ijrd.com 477
Atop band ripple (A) = 1 1+(k2 1) 2 Apa band attenuation (A P) = ( (1 k 2 ) K 2 2 K 2 1 (1) -1) (2) A. Deign of Peak and Notch Atop Band Ripple and Apa Band Attenuation K 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 0.54 0.57 0.59 0.61 0.62 0.64 0.67 0.66 A S 88 29 37 17 75 13 41 33 Table 1: Peak filter plot of Atop band attenuation vere K K 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 0.39 0.43 0.47 0.52 0.56 0.60 0.64 0.65 A p 40 49 70 00 38 83 47 35 Table 2: Peak filter Plot of Apa band ripple vere K Fig. 1: Peak B T and A P vere k K 1.1 1.2 1.3 1.4 1.5 1.8 1.9 2.0 1.46 1.35 1.25 1.15 1.06 0.86 0.81 0.76 B t 67 89 40 68 94 49 24 59 Table 3: Notch filter plot of Atop band ripple vere K K 1.1 1.2 1.3 1.4 1.5 1.8 1.9 2.0 0.32 0.08 0.01 0.00 0.00 0.08 0.11 0.15 A p 02 54 73 02 62 24 73 47 Table 4: Notch filter plot of Apa band attenuation vere K C. Decription of elliptic deign method 1) Second Order peak filter and notch filter ettling time & bandwidth The attenuation at the notch and peak frequency i ideally infinite. However, in practical circuit the attenuation i finite. Therefore, the filter i modelled by the following tranfer function: H() = 2 +ω Bw A N +ω2 o S 2 +ω BW S+ω2 o A N i the attenuation at the frequency, ωbwi the notch bandwidth and ω 0 i the notch frequency in rad/. The time repone of the filter output for a inuoidal input i Y S (t) =A Nin(ω o t) +2 ω O(A N 1)e t ω BW 2 in(t 4 ω 2 O ωbw 2 4 ω 2 o ω 2 BW The econd part i the tranient olution, which decay exponentially and where the decay time i only a function of the notch bandwidth the 2% ettling time i written a follow[8]. T S= 2 LN (.02) 2 π f BW (5) Elliptic deign i imple method. Elliptic filter offer teeper roll off characteritic than Butterworth or Chebyhev filter, but are equiripple in both the pa- and topband. In general elliptic filter meet given performance pecification with the lowet order of any filter type. Frequency i much higher than the bandwidth and the attenuation at the notch frequency i much greater than 20 db, the 20 db bandwidth of the notch filter can be approximated a: F bw20db f bw 99 (3) IV. SIMULATION PARAMETER AND RESULT At peak filter Q=2 & Q=16 and notch filter at Q=2 & Q=90000 repone like pole zero, phae delay, magnitude repone, unit tep repone, impule repone etc were plotted and the reult ha been hown. A. Q-Factor Variation in Peak for Q=2 (4) Fig. (2): Notch B T and A P vere k B. Q-Tuning By Crytal Ocillator To generate quality factor of order hundred thouand to get harp notch we ue crytal ocillator.a major reaon for the wide ue of crytal ocillator i their high Q- factor. A typical q value for a quartz ocillator range from 104 to 106, compared to perhap 102for LC ocillator. The maximum q for a high tability quartz ocillator can be etimated a q = 1.6 107/f, where f i the reonance frequency in megahertz [7]. Fig. 5: Magnitude repone for Q=2 Fig. 3: ymbol of piezoelectric crytal reonator Fig. 4: Equivalent circuit for a quartz crytal in an ocillator Fig. 6: Phae repone for Q=2 All right reerved by www.ijrd.com 478
Fig. 7: Group delay for Q=2 Fig. 12: Magnitude and phae repone for Q=2 Fig. 8: Phae delay for Q=2 Fig. 13: Magnitude repone etimate for Q= 2 Fig. 9: Impule repone for Q=2 Fig. 14: Round off noie power pectrum for Q=2 Q-FACTOR VARIATION IN PEAK FILTER FOR Q=16 Fig. 10: Step repone for Q=2 Fig. 15: Magnitude repone for Q=16 Fig. 11: Pole zero plot for Q=2 Fig. 16: Phae repone for Q=16 All right reerved by www.ijrd.com 479
Fig. 17: Group delay for Q=16 Fig. 22: Magnitude and phae repone for Q=16 Fig. 18: Phae delay for Q=16 Fig. 23: Magnitude repone etimate for Q=16 Fig. 19: Impule repone for Q=16 Fig. 24: Round off noie power pectrum for Q=16 B. Q-Factor Variation In Notch For Q=2 Fig. 20: Step repone for Q=16 Fig. (25): Magnitude repone for Q=2 Fig. 21: Pole zero plot for Q=16 Fig. (26): Phae repone for Q=2 All right reerved by www.ijrd.com 480
Fig. 27: Group delay for Q=2 Fig. 32: Magnitude and phae repone for Q=2 Fig. 28: Phae delay for Q=2 Fig. 33: Magnitude repone etimate for Q=2 Fig. 29: Impule repone for Q=2 Fig. 34: Round off noie power pectrum for Q=2 C. Q-Factor Variation In Notch For Q=90000 Fig. 30: Step repone for Q=2 Fig. 35: Magnitude repone for Q=90000 Fig. 31: Pole zero plot for Q=2 Fig. 36: Phae repone for Q=90000 All right reerved by www.ijrd.com 481
Fig. 37: Group delay for Q=90000 Fig. 41: Pole zero plot for Q=16 Fig. 38: Phae delay for Q=90000 Fig. 42: Magnitude and phae repone for Q=16 Fig. 39: Impule repone for Q=2 Fig. 43: Magnitude repone etimate for Q=16 Sl no. Freq. (MHz) Fig. 40: Step repone for Q=2 Order PEAK FILTER Quality Factor Tuning parameter (Output Gain) No. of Multiplier, Adder, State Fig. 44: Round off noie power pectrum for Q=16 At filter bandwidth gain= -3.0103db, ettling time =13.8nec, frequency bandwidth (f BW ) = 9045.3 khz comparion of the performance-peak filter and notch filter, have been given below Order Quality Factor Tuning parameter NOTCH FILTER (Output Gain) No. of Multiplier, Adder, State 1 90 4 2 1.05930 8,11,8 2 2 25.0663 7,4,2 2 90 4 4 1.06139 8,11,8 2 20 143.5311 7,4,2 3 90 4 6 1.06449 8,11,8 2 200 2407.9969 7,4,2 4 90 4 8 1.06756 8,11,8 2 2000 13390.4653 7,4,2 5 90 4 11 1.06990 8,11,8 2 40000 15995.8534 7,4,2 6 90 4 12 1.072322 8,11,8 2 80000 16028.2918 7,4,2 7 90 4 16 1.07232 8,11,8 2 90000 16028.7471 7,4,2 8 90 4 18 1.02249 8,11,8 2 100000 16029.0728 7,4,2 Table 5: Comparion of the performance-peak filter and notch filter imulation reult All right reerved by www.ijrd.com 482
V. FILTER STRUCTURE USED Direct form II tructure of IIR ytem: an alternative tructure called direct form-ii tructure can be realized which ue le number of delay element than the direct form l tructure Conider the general difference equation governing an IIR ytem. In general, the time domain repreentation of an N th order ytem i, N Y (n) = = 1a m y(n m) + = 0b m y(n m) M N M Fig. 48: Peak filter with adder, multiplier and delay element Fig. 45: Direct form I tructure Fig. 46: Direct form II tructure VI. REALIZATION OF THE NOTCH AND PEAK FILTER For the realization of 2nd order filter it require multiplier, delay and adder element. it i clear that a the order of the filter i high the computational complexity i more i.e. i more number of multiplier, adder and delay element of peak and notch filter Type of Notc h Orde r Multiplier Adder State Mpi Api 2 7 4 2 7 4 Peak 4 11 8 8 11 8 Table 6: information of order=4 and 2 i independent of Q-factor Fig. 47: The performance and cot of all the all deign have been analyed Fig. 49: Notch filter with adder, multiplier and delay element VII. CONCLUSION The deign technique for modified repone of Peak and Notch filter have been ued and their repone ha been oberved. The objective of the work i to remove the noie preent at 90 MHz fixed narrowband interference ignal which i unwanted and almot preent in communication ytem at thi frequency. The performance of Notch filter of order 2 ha been analyed for Q-factor 2 100000 and repone ha been oberved a Notch filter harpne increae and bet Notch filter ha been occurred at Q= 90000 and wort performance with introduction of error ha been occurred at Q=2.For Quality factor Q=100000 and beyond diturbance and error have been een in Notch filter and hence it ha been retricted. The performance of Peak filter of order 4 ha been analyed for Q-factor having range from 2 18 and repone ha been oberved a Peak filter harpne increae and bet Peak filter ha been occurred at Q= 16 and wort performance with introduction of error ha been occurred at Q=2. For Quality factor Q=18 and beyond diturbance and error have been een in Peak filter and hence it ha been retricted. Comparion between performance for Peak and Notch filter how that peak filter ha better repone at lower value of quality factor than that of Notch filter.thee Notch and Peak filter can be realized by a computationally efficient lattice tructure with minimum number of multiplier (7), adder (4), no. of tate (2), multi per input ample (7) and add per input ample (4) for Notch filter and with minimum number of multiplier (11), adder (8), no. of tate (8), multi per input ample (11) and add per input ample (8) for Peak filter. REFERENCES [1] J. Dattoro, Effect deign, the frequencie that we want to reject, retain or emphaize amplitude of the partial and other filter. J. Audio Eng. Soc., 45(9):660-684, September 1997 [2] J. Pikorowki, Digital Q-varying notch IIR filter with tranient uppreion, IEEE Tran. on intrumentation and meaurement, vol. 59, No.4, Apr., 2010 All right reerved by www.ijrd.com 483
[3] Pardeepkaur, imarpreetkaur, to improve the magnitude repone, pa band and top band in FIR filter uing GA, IJAIEM, vo. 2, iue 1, January 2013. [4] J. S. Silva, P. F. Silva, A. Fernandez, J. Diez, and J. F. M. Lorga, Factored Correlator Model: A olution for fat, flexible, and realitic elliptic deign imulation, in Proc. ION/GNSS, 2008. [5] Amandeep kaurmaan, balraj ingh, darhan. Sidhu, deign of high order digital IIR uing heuritic optimization technique, IJARCSSE, vol. 4, iue 10, October 2014. [6] C. Charoenlarpnopparut, P. Charoen, A. Thamrongma, S. Samurpark and P. Boonyanant, High-Quality factor, double notch, IIR digital filter deign uing optimal pole re-poition technique with controllable paband gain, IEEE, 2009. [7] Jacob mill man, chritoc.halkia, Integrated Electronic, page-no.-495. [8] Y.V.Johi and S.C.Duttaroy, Circuit Sytem Signal Proceing, vol.16, no.4, 1997, pr. 415-427. All right reerved by www.ijrd.com 484