International Journal of Scientific Research Engineering & Technology (IJSRET)Volume 2 Issue 6 pp 358-361 September 2013 www.ijsret.org ISSN 2278 – 0882

IJSRET @ 2013

IIR Filter Design and Analysis using Notch and Comb Filter

Monika Singh Saroj Dogra Rajesh MehraM.E. Student (ECE) M.E. Student (ECE) Associate Professor (ECE)NITTTR, Chandigarh, India NITTTR, Chandigarh, India NITTTR, Chandigarh, India

ABSTRACTDigital IIR Notch and IIR Comb filters are employed invarious communication systems to eliminate unwantednarrow band interference of unwanted frequencies. In thispaper the cost analysis and resource analysis of both thefilters has been done. The Notch and Comb filter havebeen designed on Simulated MATLAB. The result showsthat Comb filter provides a reduction in 83.35% ofmultipliers and 87.50% of adders as compared to Notchfilter.

Keywords- Notch, Comb, Adders, Multipliers, QualityFactor

I. INTRODUCTIONFilters are analog circuits which performs signalprocessing function. It is used to specially removeunwanted frequency components from the signal toenhance wanted ones or both. Electronic filters can be:

passive or active analog or digital High-pass, low-pass, band pass, band-reject (band

reject; notch), or all-pass. discrete-time (sampled) or continuous-time linear or non-linear infinite impulse response (IIR type) or finite

impulse response (FIR type)

A band stop filter designed to block a single frequencycomponent is called a notch filter. In a signal processing, acomb filters adds a version of signal itself .it causesconstructive and destructive interference, the frequencyresponse of a comb filter consist of a series of regularlyspaced spikes, which gives the appearance of a comb.

In signal processing, a band-stop filter or band-rejection filter is a filter that passes most frequenciesunaltered, but attenuates those in a specific range to very

low levels. A notch filter is a band-stop filter with anarrow stop band and high quality factor. The notch filteris to designed to attenuate a particular frequencycomponent and has a narrow notch width, Practically,notch filter is used for eliminating the unwanted singlefrequency or sinusoidal interference and there are manyapplications of notch filter, e.g. in the field of signalprocessing, in electrocardiograms to removing the powerline interferences, in broadcast TV to cancelling noise, etc.Narrow notch filters are used in Raman spectroscopy inoptical communication, live sound reproduction in publicaddress systems and in instrument amplifiers especiallyamplifiers or preamplifiers for acoustic instruments suchas acoustic guitar, mandolin, bass instrument amplifier,etc. to reduce or prevent audio feedback

A comb filter is designed to block the frequenciesthat are integral multiples of a low frequency. A combfilter has a frequency response that is periodic function ofω with a period 2пL, where L is the notch frequency in therange of 0 ≤ w ≤ 2π. The comb filter is so called asbecause the frequency response of a comb filter consists ofa series of regularly spaced spikes, giving the appearanceof a comb. Comb filter is an example of filters withmultiple pass bands and stop bands. Comb filter withmultiple notches frequencies are used in cancellation ofperiodic interference. These are also used in LONARnavigation system for the suppression of cross rateinterference. It is also used in digital colour televisionreceivers for separating the luminance components fromintensity information and chrominance components whichcontains the colour information. Cascaded Integrator-Comb filters, commonly used for anti- aliasing duringinterpolation and decimation operations that change thesample rate of a discrete-time system, 2D and 3D combfilters used in PAL and NTSC television systems decoder.

International Journal of Scientific Research Engineering & Technology (IJSRET)Volume 2 Issue 6 pp 358-361 September 2013 www.ijsret.org ISSN 2278 – 0882

IJSRET @ 2013

II. SYSTEM MODELThe digital IIR Notch filters are generally used in becauseof its lower order has a narrow stop band with high qualityfactor. The magnitude of an ideal IIR notch filter can berepresented as:

(1)

Where (і=1 to N), N indicates a notch frequencies. Thetransfer function of a single frequency notch filter having anotch at of bandwidth B can be expressed as:

(2)Where

(3)

The components and are given by

(4)

(5)

Comb filter are of two types: feedforword and feedback.

Feedforward form:

Fig1: Feedforword Comb Filter

In equation form feedforword form can be expressed bythe difference equation:

y(n) = x(n) + αx(n-M) (6)

Where ‘M’ is delay length and ‘α’ is the scaling factorapplied to the delayed signal. By taking Z Transform onboth sides

(7)

Equation for frequency response of discrete-time systemexpressed by substituting z= ejω . Therefore the frequencyresponse for feedforword comb filter

(8)

By Euler’s formula, frequency response is given by:

(9)

And its magnitude response is given by

(10)

Here (1+α2) is a constant term where as term 2αcos(⍵k)varies periodically. Thus the magnitude response of thecomb filter is periodic. The response periodically drops toa minimum value, and periodically rises to a maximumvalue. For positive values of α, the first minimum occurs athalf the delay period and repeat at odd multiples of thedelay frequency i.e

(11)

The feedforward comb filter is one of the simplest finiteimpulse response (FIR) filters. Transfer function of thefeedforward comb filter is given by:

(12)

Feedback form:

Fig2: Feedback form Comb FilterGeneral equation for feedback form is

y(n) = x(n) + αy(n-M) (13)

α

+ y(n)

Delay

x(n)

Delay α

+x(n)y(n)

International Journal of Scientific Research Engineering & Technology (IJSRET)Volume 2 Issue 6 pp 358-361 September 2013 www.ijsret.org ISSN 2278 – 0882

IJSRET @ 2013

The transfer function of feedback form is:

(14)and the frequency response is given by

(15)

And the magnitude response is given by:

(16)

The feedback filter has some properties common to feedforward form that is: The response periodically drops to alocal minimum and rises to a local maximum. The maximafor positive values of α coincide with the minima fornegative values of α, and vice versa. For positive valuesof α, the first minimum occurs at 0 and repeats at evenmultiples of the delay frequency i.e.

(17)

The feedback The feed backward comb filter is a simple type of infiniteimpulse response (IIR) filter. If stable, the responsesimply consists of a repeating series of impulsesdecreasing in amplitude over time.

III. SIMULATION RESULTSNotch filters are useful to eliminate the particularlyfrequency component at a certain frequency. For IIR notchfilter to eliminate “80” Hz interference frequency in asignal sampled at “1000”Hz filter order of “ 8” and qualityfactor of “100” is taken. The quality factor or Q-factor ofthe filter is a measure of how the desired frequency isisolated from other frequency for a fixed filter order; ahigher Q-factor is accomplished by pushing the polescloser to the zero. Now result is determined by the use ofMATLAB function.

The frequency response of a comb filter consistsof regularly spaced spikes and giving the appearance of acomb In this analysis, sampling frequency, filter order andquality factor is taken as same as the above notch filter,attenuation pass band is 1 and bandwidth(BW) is2*Fs/2/8/Q.

Analysis of combine IIR notch and IIR comb filter takenas the same parameters as above.

Fig3: Frequency response of IIR notch filter

Fig4: Frequency response of IIR comb filter

International Journal of Scientific Research Engineering & Technology (IJSRET)Volume 2 Issue 6 pp 358-361 September 2013 www.ijsret.org ISSN 2278 – 0882

IJSRET @ 2013

Fig5: Frequency response of combine IIR notch and IIRcomb filter

TABLE: Design parameters

PARAMETERS IIR NOTCHFILTER

IIR COMBFILTER

Multipliers 18 3

Adders 16 2

No. of states 8 8Multi per inputsample 18 3Add per inputsample 16 2

V. CONCLUSION

In this paper the implementation of cost for IIR notch andIIR comb filter has been analyzed. The number of addersand multipliers are 16 and 18 in IIR notch filter even thecase of IIR comb it is only 2 and 3.Filter required for filterorder 8, sample frequency 1000 and Quality factor 100.The IIR comb filter is much cost efficient in comparison ofIIR notch filter.

REFERENCE[1] S. K. Mitra, "Digital Signal Processing AComputer-Base Approach", McGraw-Hill, 2001.

[2] J. G. Proakis and D. G. Manolakis, "Digital SignalProcessing Principle, Algorithms, and Applications",Prentice Hall, 1996.

[3] A. Thamrongmas and C. Charoenlarpnopparut, "ANovel Design of IIR Multiple Notch Filter Based onAll-pass Filter by Pole-reposition Technique".

[4] Yashwant Y. Joshi and S. C. Dutta Roy, "Designof I1R Multiple Notch Filters Based on All-PassFilters", IEEE Trans. on Circuits and Systems II:Analog and Digital Signal Processing, Vol. 46, No. 2,February, 1999.

[5] Li Jia-hui, Wang-heng, Jin Yu-hong, “One Combfilter for lower power consumption”, 2012.

[6] J.L.Rasmussen, “New Method of FIR Comb Filtering.