DOI : 10.17577/IJERTV2IS120211
- Open Access
- Total Downloads : 515
- Authors : Priyanka Das, Mousumi Karmakar
- Paper ID : IJERTV2IS120211
- Volume & Issue : Volume 02, Issue 12 (December 2013)
- Published (First Online): 06-12-2013
- ISSN (Online) : 2278-0181
- Publisher Name : IJERT
- License:
This work is licensed under a Creative Commons Attribution 4.0 International License
A New Window Function to Design FIR Filter with an Improved Frequency Response for Suppressing Side-Lobe Attenuation and Study Comparison with the Other Windows
Priyanka Das1 and Mousumi Karmakar2
1Assistant Professor of Electronics and Communication Engineering MallabhumInstitute of Technology,P.S: Bishnupur, Dist: Bankura-722122,W.B.,India
2Assistant Professorof Electronics and Communication Engineering MallabhumInstitute of Technology, P.S: Bishnupur, Dist: Bankura-722122, W.B.,India
Abstract
In both digital filter design and spectral estimation, the choice of a windowing function can play an important role in determining the quality of overall results. The main role of the window is to damp out the effects of the Gibbs phenomenon that results from truncation of an infinite series. There are various types of window techniques. In many applications like filter design, FFT, beam forming, signal processing and measurements it is seen that particular one type of filter is not applicable for all purpose. This paper presents a new window technique which has better performance compared to commonly used window like Hamming, Hanning & Blackman window. The simulation result where the advantage of this proposed window is shown is actually the minimization of side lobes& ripples. The simulation is done in Matlab 12. The Matlab program returns with a satisfactory result with proper magnitude plotting& filter response.
(Keywords:FIR, Hamming, Hanning, Blackman, Proposed Window, Window method)
-
INTRODUCTION
Digital filter plays an important role in digital signal processing applications such as digital signal filtering, noise filtering, signal frequency analysis, speech and audio compression, biomedical signal processing and image enhancement etc. A digital filter is a system which passes some desired signals more than others to reduce or enhance certain aspects of that signal. It can
be used to pass the signals according to the specified frequency pass-band and reject the frequency other than the pass-band specification. The basic filter types can be classified into four categories: low-pass, high-pass,
band-pass, and band-stop. On the basis of impulse response, there are two fundamental types of digital filters: Infinite Impulse Response (IIR) filters, and Finite Impulse Response (FIR) filters [1].
FIR filters are filters having a transfer function of a polynomial in z- and is an all-zero filter inthe sense that the zeroes in the z-plane determine the frequency response magnitudecharacteristic. The z transform of aN-point FIR filter is given by[9]
=
=
H (z) = ———(1)
FIR filters are particularly useful for applications where exact linear phase response is required. The FIR filter is generally implemented in a non-recursive way which guarantees a stable filter. FIR filter design essentially consists of two parts[5][6][7]
-
Approximation problem
-
Realization problem
The approximation stage takes the specification and gives a transfer function through four steps. They are as follows:
-
A desired or ideal response is chosen, usually in the frequency domain.
-
An allowed class of filters is chosen (e.g. the length
N for a FIR filters).
-
A measure of the quality of approximation is chosen.
(iv)A method or algorithm is selected to find the best filter transfer function.
The realization part deals with choosing the structure to implement the transfer function which may be in the form of circuit diagram or in the form of a program. There are essentially three well-known methods for FIR filter design namely:
-
The window method
-
The frequency sampling technique
-
Optimal filter design methods
In this paper attention is given only for window method. Here proposed window method is compared with the commonly used window like Hamming, Hanning&Blackman window along with their frequency responses in case of various types of FIR
1
0.9
0.8
0.7
Amplitude
Amplitude
0.6
0.5
0.4
0.3
0.2
0.1
0
Hanning Window Response
N=63
filter.
-
-
DIFFERENT WINDOW TECHNIQUE
0 10 20 30 40 50 60 70
Samples
Fig.2.1.a
Window technique involves a function called window function or apodization function which states that if some interval is chosen, it returns with finite non-zero value inside that interval and zero value outside that interval[8]. So, if the window with chosen interval is applied on the IIR system, it will obviously return with a finitenon-zero value inside that interval producing a FIR system and all other value that is outside the interval willbe zero. So, we can view the finite response inside some predefined interval.Some of the windows
-
commonly used are as follows:
-
HANNING WINDOW
The Hanning window is one type of raised cosine window. The equation for Hanning window sequence is
40
30
Normalized magnitude
Normalized magnitude
20
10
0
-10
-20
N=63
N=63
Frequency response of Hanning Window
written as [3][4][10]
. .
; =
-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2
Normalized frequency (w/pi)
Fig.2.1.b
whn() =
———(2)
;
-
HAMMING WINDOW
Hamming window is most commonly used window in
Where N= no. of sample of the window.In this paper for all type of window response N is taken as 63. The
speech processing. It is given as: [3][4][10]
. . ; = .
Hanning window sequence&its frequency response is presented in Fig.2.1.a & Fig.2.1.b respectively using MATLAB 2012 software package.
wh(n) =
———(3)
;
The Hamming window sequence is shown in Fig.2.2.a. Its first & last samples are not zero. The frequency response of this window for N (no. of samples) = 63, is shown in Fig.2.2.b.
1
0.9
0.8
0.7
Amplitude
Amplitude
0.6
0.5
0.4
0.3
0.2
0.1
0
Hamming Window Response
N=63
1
0.9
0.8
0.7
Amplitude
Amplitude
0.6
0.5
0.4
0.3
0.2
0.1
0
Blackman Window Response
N=63
0 10 20 30 40 50 60 70
0 10 20 30 40 50 60 70
Samples
Fig.2.2.a
Samples
Fig.2.3.a
40
30
Normalized magnitude
Normalized magnitude
20
10
0
-10
Frequency response of Hamming Window
30
25
20
Normalized magnitude
Normalized magnitude
15
10
5
0
-5
-10
-15
Frequency response of Blackman Window
N=63
N=63
-20
-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2
Normalized frequency (w/pi)
Fig.2.2.b
-20
N=63
N=63
-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2
Normalized frequency (w/pi)
Fig.2.3.b
-
BLACKMAN WINDOW
The Blackman windowwB(n) is another type of cosine window defined by the equation[3][4][10]
w (n)= 0.42- 0.5 cos +0.08cos ;
-
PROPOSED WINDOW
-
In this section proposed window function is presented. It is defined as [3][4][10]
B
w(n) = . . + .
for n=0 to N-1———(4)
Blackman window sequence &its frequency response for N= 63 is presented in Fig.2.3.a & Fig.2.3.b respectively.
= ———(5)
The proposed window sequence & its frequency response for N= 63 is presented in Fig.2.4.a & Fig.2.4.b respectively.
1.4
1.2
1
Amplitude
Amplitude
0.8
0.6
0.4
0.2
Proposed Window Response
N=63
1.4
1.2
1
Amplitude
Amplitude
0.8
0.6
0.4
0.2
0
Different Window Response
0
0 10 20 30 40 50 60 70
Samples
Fig.2.4.a
Frequency response of Proposed Window
N=63
N=63
40
30
-0.2
Blackman
Hamming
Hanning Proposed
Blackman
Hamming
Hanning Proposed
0 10 20 30 40 50 60 70
Samples
Fig.3.a
According to Fig.3.a, the specification of different window sequence is given in Table.1.
Table.1
Type of
Normalized magnitude
Normalized magnitude
20 Window
(for N=63)
10
Maximum Amplitude of Window
Minimum Amplitude of Window
0
-10
-20
-30
-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2
Normalized frequency (w/pi)
Fig.2.4.b
Blackman 1.0 0
Hanning 1.0 0.08
Hamming 1.0 0
Proposed 1.36 0
Now to verify the specifications of proposed window more briefly,frequency domain analysis is required & this is done in MATLAB 12 by using proper command.
-
-
COMPARE BETWEEN PROPOSED WINDOW & OTHER WINDOWS
In this section, performance of the proposed window with several commonly used windows is compared using Matlab12 which is shown in Fig.3.a
100
Normalized magnitude in dB
Normalized magnitude in dB
50
0
-50
Log-Magnitude response of Different Window
Blackman
Hammin Hanning
Proposed
Blackman
Hamming Hanning
Proposed
-100
-150
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized frequency (w/pi)
Fig.3.b
The value which is collected from Fig.3.b is shown in Table.2.
Type of Window (for N=63)
Approximate Width of Main Lobe
Magnitude of 1st side Lobe
Range of Stopband Ripple
Blackman
0.064(w/)
-70dB
-70 to
-140 dB
Hanning
0.057(w/)
-5dB
-5 to -120
dB
Hamming
0.057(w/)
-30dB
-25 to
-110 dB
Proposed
0.067(w/)
-61dB
-61 to
-124 dB
Type of Window (for N=63)
Approximate Width of Main Lobe
Magnitude of 1st side Lobe
Range of Stopband Ripple
Blackman
0.064(w/)
-70dB
-70 to
-140 dB
Hanning
0.057(w/)
-5dB
-5 to -120
dB
Hamming
0.057(w/)
-30dB
-25 to
-110 dB
Proposed
0.067(w/)
-61dB
-61 to
-124 dB
Table.2
0
-100
-200
Magnitude(dB)
Magnitude(dB)
-300
-400
-500
Low pass FIR filter
-
PERFORMANCE ANALYSIS OF PROPOSED WINDOW WITH OTHER WINDOWS
In this section the modified window function w(n), as in equation (5) is compared with the other windows along with their frequency responses in case of various types of digital FIR filter. To study the efficiency of the proposed window we have compared the results by observing the Fourier Transform of a low pass, high pass, band pass & band stop FIR filter designed by truncating of an ideal IIR low pass filter.
-
LOW PASS FILTER RESPONSE
The impulse response of an ideal low pass filter is taken as [1],[3]:
hd(n) = sin Ac/ A———(6) where, A= n-a+k
k=0.001, a=(N-1)/2, n=1,2,—–,N-1
N= 63 (no. of sample) c = 0.5 (cut-off frequency)
The low pass filter response is shown in Fig.4.1.a &
detailed specifications are given in Table.3.
-600
Ham
ming
Prop
osed
Han
ning
Blac
kman
Ham
ming
Prop
osed
Han
ning
Blac
kman
-700
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized frequency (w/pi)
Fig.4.1.a
Table.3
Type of window for low pass
FIR filter
Cut-off frequency (c)
Stop-band attenuation range (Approx.)
Roll-off rate
Hanning
0.5
-450 to
-583dB
Low
Hamming
0.5
-100 to
-245dB
Low
Blackman
0.5
-465 to
-600dB
Medium
Proposed
0.5
-150 to
-280dB
Medium
-
HIGH PASS FILTER RESPONSE
The impulse response of an ideal high pass filter is taken as: [1],[3]
hd(n) = (sin A-sin Ac) / A———(7) where,A= n-a+k
The high pass filter response using various window techniques along with proposed window is shown in Fig.4.2.a & detailed specifications are given in Table.4.
0
-100
High pass FIR filter
International Journal of Engineering Research & Technology (IJERT)
ISSN: 2278-0181
Vol. 2 Issue 12, December – 2013
Magnitude(dB)
Magnitude(dB)
Blackman
Hamming
Hanning Proposed
Blackman
Hamming
Hanning Proposed
-200
-300
-400
-500
0
-100
-200
Magnitude(dB)
Magnitude(dB)
-300
-400
Band pass FIR filter
-600
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized frequency (w/pi)
Table.4
-500
-600
range (Approx.)
range (Approx.)
Window for high pass
FIR filter
Cut-off frequency (c)
Stop-band attenuation
Fig.4.2.a
Roll-off rate
Hanning
0.5
-440 to
-560dB
Low
Hamming
-100 to
-215dB
Low
Blackman
0.5
-465 to
-580dB
Medium
Proposed
0.5
-150 to
-260dB
Medium
Window for high pass
FIR filter
Cut-off frequency (c)
Stop-band attenuation
Fig.4.2.a
Roll-off rate
Hanning
0.5
-440 to
-560dB
Low
Hamming
0.5
-100 to
-215dB
Low
Blackman
0.5
-465 to
-580dB
Medium
Proposed
0.5
-150 to
-260dB
Medium
-700
Blackman Hamming
Hanning
Proposed
Blackman Hamming
Hanning
Proposed
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized frequency (w/pi)
Fig.4.3.a
-
BAND PASS FILTER RESPONSE
The impulse response of an ideal band pass filter is taken as: [1],[3]
hd(n) = (sin Ac2-sin Ac1) / A ————(8) where, A=n-a+k
c1 = Lower cut-off frequency c2 = Upper cut-off frequency
The band pass filter response using various window techniques along with proposed window is shown in Fig.4.3.a & detailed specifications are given in Table.5
Table.5
Window for Bandpass FIR filter
c1
c2
Stop-band attenuati- on range (Approx.)
Roll off rate
Hanning
0.4
0.65
-450 to
-600dB
Low
Hamming
0.4
0.65
-100 to
-230dB
Low
Blackman
0.4
0.65
-470 to
-615dB
Medium
Proposed
0.4
0.65
-160 to
-305dB
Medium
-
BAND STOP FILTER RESPONSE
The impulse response of an ideal band pass filter is taken as: [1],[3]
hd(n) = (sinA- (sin Ac1-sin Ac2) )/ A ——(9) where, A= n-a+k
c1 = Lower cut-off frequency c2 = Upper cut-off frequency
The band stop filter response using various window techniques along with proposed window is shown in Fig.4.4.a & detailed specifications are given in Table.6
0
-100
Magnitude(dB)
Magnitude(dB)
-200
-300
-400
-500
-600
Band stop FIR filter
Blackman Hamming
Hanning
Proposed
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized frequency (w/pi)
Fig.4.4.a
Window for Bandstop FIR filter
c1
c2
Stop-band attenuation range (Approx.)
Roll off rate
Hanning
0.4
0.65
-445 to
-550dB
Low
Hamming
0.4
0.65
-98 to
-200dB
Low
Blackman
0.4
0.65
-460 to
-570dB
Medium
Proposed
0.4
0.65
-140to
-240dB
Medium
Window for Bandstop FIR filter
c1
c2
Stop-band attenuation range (Approx.)
Roll off rate
Hanning
0.4
0.65
-445 to
-550dB
Low
Hamming
0.4
0.65
-98 to
-200dB
Low
Blackman
0.4
0.65
-460 to
-570dB
Medium
Proposed
0.4
0.65
-140to
-240dB
Medium
Table.6
-
FUTURE WORK
In this paper we have designed a new window function which minimizes the side lobe ripples as well as produces good frequency response for low pass, high pass, band pass & band stop FIR filter. But the power consumption rate of this proposed window is not better than Blackman window. Therefore in future, stress will be given for the improvement of this proposed window function so that power consumption rate is decreased than other window techniques.
-
REFERENCES
:Principles, Algorithms andApplications, Prentice- Hall,EnglewoodcliffsNJ,secondedition,1992.
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Sanjay Sharma; Digital Signal Processing;
KatsonBooks.
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P.RameshBabu;DigitalSignalProcessing; Scitech.
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Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing. Upper Saddle River, NJ: Prentice- Hall, 1999, p. 468.Oppenheim, A.V., and R.W. Schafer, Discrete-Time Signal Processing, Prentice-Hall, 1989, pp. 447-448.
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MdAbdusSamad A novel window function yielding suppressed mainlobe width and minimum sidelobe peak International Journal of Computer Science, Engineering andInformation Technology (IJCSEIT), Vol.2, No.2, April 2012.
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-
-
CONCLUSION
Performancecomparisonoftheproposedwindowcompare dtothatoftheHanning, HammingandBlackmanwindowshows thattheproposed windowofferssuppressedstop band attenuationwiththeother window techniques. This is the major advantage of proposed window. Also this window has slightly greater main lobe width compared to Hanning, Hamming & Blackman window. Again it is known to us that if roll-off rate increases the sharpness of window increases. It is seen that the proposed window offers faster roll-off rate compared to Hanning& Hamming window but its roll-off rate is same like Blackman window.
-
Peformance Analysis of Finite Impulse Response(FIR) Filter Design Using Various Window Methods; Era Singhal; International Journal of Scientific Research Engineering & Technology (IJSRET); Volume 1 Issue 5 pp 018-021 August 2012; ISSN 2278 0882.
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Comparison of Band-stop FIR Filter using Modified Hamming Window and Other Window functions and Its Application in Filtering a MutitoneSignalISSN: 2278- 1323 bySaurabh Singh Rajput, Dr. S.S. Bhdauria.International Journal of Science, Engineering and Technology Research (IJSETR) Volume 2, Issue 8, 2012.
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SonikaGupta, AmanPanghal; Performance Analysis of FIR Filter Design by Using Rectangular ,Hanning and Bartlett-HannWindows Methods,Volume2, Issue6, June 2012ISSN: 2277128X International Journal of Advanced Research in Computer Science and Software Engineering (IJARCSSE).
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Ha,Y.H., and J.A. Pearce;"A new Window and Comparison to Standard Windows ."IEEE® Transactions on Acoustics, Speech, and Signal
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S.Salivahanan, A.Vallavaraj,C. Gnanapriya, Digital Signal Processing, Tata McGraw-Hill, 2000
AUTHORS
PriyankaDas received B.Tech (2009) degree in Electronics and Instrumentation Engineering &M.Tech (2011) degree in Mobile Communication & Networking from JIS College of Engineering,Kalyaniunder West Bengal University of Technology. She is presently working as an Asst. Professor of Department of Electronics and Communication Engg. AtMallabhum Institute of Technology, Bishnupur, Dist: Bankura-722122, W.B., India.Her area of interestsinclude Signals & Systems, Digital signal processing, Control System, Electronics Circuit design etc.
MousumiKarmakar received B.E (2005) degree in Electronics and Communication Engineering fromUniversity Institute of Technology, Golapbagh, Burdwan under Burdwan University. She obtained M.Tech (2008) in Mechatronics Engg. from NITTTR, Salt-lake, Kolkata under West Bengal University of Technology. She is presently working as an Asst. Professor of Department of Electronics and Communication Engg. atMallabhum Institute of Technology, Bishnupur, Dist: Bankura-722122, W.B., India.Her area of interests include Signals & Systems, Digital signal processing, Microprocessors & Microcontrollers, Electronics Circuit design design etc.