 Open Access
 Total Downloads : 405
 Authors : Manira Khatun
 Paper ID : IJERTV3IS20222
 Volume & Issue : Volume 03, Issue 02 (February 2014)
 Published (First Online): 13022014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Design Technique of LowPass Filter Using Different Window
Manira Khatun
Assistant Professor, Department of Electronics and Communication Engineering, Mallabhum Institute of Technology P.S: Bishnupur, Dist: Bankura722122, W.B, India
AbstractIn the field of signal processing and communication, digital filter plays pivotal role. Digital FIR filter designed by different window techniques perform better for reducing noise from signal. In this paper , we design lowpass filter by using various window methods such as Hanning, Hamming, Blackman, Kaiser .This paper also provides comparative study of lowpass filters using above window. It has been seen that Kaiser window is better with respect to Hanning, Hamming, Blackman window.
Keyword – Blackman window, FIR filter, Hamming window, Hanning window, Kaiser window, Lowpass filter, MATLAB .

INTRODUCTION
In different areas digital filter design techniques are widely used. In the digital filter, the input and output signals are digital or discrete time sequence. Digital filters are categorized in two parts as finite impulse response (FIR) and infinite impulse response (IIR). According to the frequency characteristics digital filter can be dividedlowpass, highpass, bandpass, and bandstop. Filtering can be applied to perform

The window method

The frequency sampling technique

Optimal filter design methods [2]

Window design method
The window design method is first designs an ideal IIR filter and then truncates the infinite impulse response by multiplying it with a finite length window function. The result is a finite
impulse response filter whose frequency response is modified from that of the IIR filter. Multiplying the infinite impulse by the window function in the time domain results in the frequency response of the IIR being convolved with the frequency response of the window function.[3]
Some of the windows commonly used are as follows:

Hanning window : The Hanning window is a raised cosine window . The hanning window is defined as


0.5 0.5 2n
applications such as noise reduction, frequency boosting, digital audio equalizing, and digital crossover, among others.
w(n)=
1
0 , elsewhere
, for n = 0 to M 1


FIR DIGITAL FILTER
Finite impulse response (FIR) filter is a filter whose impulse response is of finite duration, because it settles to zero in finite time. This is in contrast to infinite impulse response (IIR)

Hamming window: The hamming window is also a raised cosine window. The hamming window is defined as
0.54 0.46 2n
filters, which may have internal feedback and may continue to respond indefinitely.
w(n)=
1
0 , elsewhere
, for n = 0 to M 1
FIR filters offer the following advantages over the IIR filters:

They can have an exact linear phase.

They are always stable.

The design methods are generally linear.


Blackman window: The Blackman window is defined as
0.42 0.5 2n + 0.08 4n

They can be realized efficiently in hardware. v.The filter startup transients have finite duration. [1]
w(n)=
0 ,
0 to M 1
1
elsewhere
M 1
, for n =
A. Fir Filter design
To design a filter means to select the coefficients such that the system has specific characteristics. The required characteristics are stated in filter specifications. Most of the


Kaiser window: The Kaiser window with parameter is defined as [2]
1(n )2
time filter specifications refer to the frequency response of the filter. There are essentially three wellknown methods for FIR filter design namely:
w(n)=
0 to M 1
()
0 , elsewhere
, for n =


DESIGN TECHNIQUE OF LOWPASS FIR FILTER USING
VARIOUS WINDOW FUNCTION :
A. Filter Specifications:
Parameters
Values
Filter Type
Lowpass
Design method
FIR windows(=0.37 for
Kaiser window only)
Filter order
30,40
Sampling frequency
48000HZ
Cutoff frequency
10800HZ
Table.1 Filter specification
0
5
Phase (radians)
10
15
20
25
30
Phase Response
hann40

RESULT AND SIMULATION

Haanning window:
From the table.1, we analyzed the lowpass filter using Hanning window in MATLAB and the response of the filter is given in fig.1 &fig.2 respectively at the order 30 &40.
35
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Normalized Frequency ( rad/sample)
Fig.2b Phase response of LPF using Hanning window of order40

Hamming window:
From the table.1, we analyzed the lowpass filter using Hamming window in MATLAB and the response of the filter is given in fig.1 &fig.2 respectively at the order 30 &40.
Magnitude Response (dB)
0
10
20
Magnitude (dB)
30
40
50
60
70
80
90
Magnitude Response (dB)
hann30
0 5 10 15 20
Frequency (kHz)
Fig.1a Magnitude response of LPF using Hanning window of order30
0
10
Magnitude (dB)
20
30
40
50
60
70
80
ham
30
/td> 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Normalized Frequency ( rad/sample)
Fig.3a Magnitude response of LPF using
Hamming window of order30
0
5
Phase (radians)
10
15
20
25
Phase Response
ha
nn30
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Normalized Frequency ( rad/sample)
Fig.1b Phase response of LPF using Hanning window of order30
0
5
Phase (radians)
10
15
20
25
Phase Response
ha
m30
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Normalized Frequency ( rad/sample)
Fig.3b Phase response of LPF using
Hamming window of order30
0
Magnitude (dB)
20
40
60
80
Magnitude Response (dB)
han
n40
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Normalized Frequency ( rad/sample)
Fig.2a Magnitude response of LPF using
Hanning window of order40
0
10
Magnitude (dB)
20
30
40
50
60
70
Magnitude Response (dB)
ha
m40
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Normalized Frequency ( rad/sample)
Fig.4a Magnitude response of LPF using
Hamming window of order40
0
5
Phase (radians)
10
15
20
25
30
35
Phase Response
ha
m40
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Normalized Frequency ( rad/sample)
Fig.4b Phase response of LPF using
Hamming window of order40
0
5
Phase (radians)
10
15
20
25
30
35
40
Phase Response
blm
an40
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Normalized Frequency ( rad/sample)
Fig.6b Phase response of LPF using Blackman window of order40

Blackman window:
From he table.1, we analyzed the lowpass filter using Blackman window in MATLAB and the response of the filter is given in fig.1 &fig.2 respectively at the order 30 &40.

Kaiser window:
From the table.1, we analyzed the lowpass filter using Kaiser window in MATLAB and the response of the filter is given in fig.1 &fig.2 respectively at the order 30 &40.
0
20
Magnitude (dB)
40
60
80
100
Magnitude Response (dB)
blm
an30
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Normalized Frequency ( rad/sample)
Fig.5a Magnitude response of LPF using Blackman window of order30
0
10
Magnitude (dB)
20
30
40
50
60
70
Magnitude Response (dB)
kai
30
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Normalized Frequency ( rad/sample)
Fig.7a Magnitude response of LPF using
Kaiser window of order30
0
5
Phase (radians)
10
15
20
25
30
Phase Response
blman30
0
Phase (radians)
5
10
15
20
kai
30
Phase Response
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Normalized Frequency ( rad/sample)
Fig.5b Phase response of LPF using
Blackman window of order30
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Normalized Frequency ( rad/sample)
Fig.7b Phase response of LPF using
Kaiser window of order30
0
20
Magnitude (dB)
40
60
80
100
Magnitude Response (dB)
blm
an40
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Normalized Frequency ( rad/sample)
Fig.6a Magnitude response of LPF using Blackman window of order40
0
10
Magnitude (dB)
20
30
40
50
60
70
Magnitude Response (dB)
kai
40
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Normalized Frequency ( rad/sample)
Fig.8a Magnitude response of LPF using
Kaiser window of order40
0
5
Phase (radians)
10
15
20
25
30
Phase Response
kai
40
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Normalized Frequency ( rad/smple)
Fig.8b Phase response of LPF using
Kaiser window of order40
Table2
Window technique
Ord er of
the filter
Width of main lobe
No. of
side lobes
Relative side lobe
attenuati on (dB)
Hanning
window
30
0.09375
7
31.5
40
0.070313
10
Hamming
window
30
0.085938
7
41.7
40
0.0625
9
Blackman
window
30
0.10938
5
58.1
40
0.082031
8
Kaiser
window
30
0.054688
9
13.5
40
0.042969
11
Comparison between various window:
REFERENCES

Digital Signal Processing; S.Salivahanan

Digital Signal Processing; Sanjay Sharma, Katson Books.

FIR Filter, Available: http://en.wikipedia.org/wiki/Finite_impulse_response

AUTHOR:
MANIRA KHATUN: She achieved her B.Tech (2007) and M.Tech (2010) degrees in Electronics & Communication Engineering under West Bengal University of Technology. She has nearly four years teaching experience in Electronics and Communication related subjects. She is presently serving as an Assistant Professor, Department of Electronics and Communication Engineering at Mallabhum Institute of Technology, Bishnupur, Bankura, West Bengal, India.
From the table 2 we can see that as the order of the FIR filter increases the number of the side lobes also increases and width of the main lobe is decreased, that it is tending to sharp cut off that is the width of the main lobe decreased. If the width of the main lobe reduces then the number of the side lobes gets increased. So there should be a compromise between attenuation of side lobes and width of main lobe. On comparing all methods, the Blackman has the smallest side lobes at any order but the width of the main lobe is increased. In the Kaiser window for the lower order the width of the major lobe is less than the other windows. The Kaiser window gives best result. Therefore it is most commonly used window for FIR filter design.


CONCLSION
Digital filter plays a very important role in different digital signal processing applications. In Kaiser window, the main lobe width is 0.054688 for filter order 30 which means this window has less transition width and introduces more ripple. Digital filter can play a major role in speech signal processing applications such as, speech filtering, speech enhancement, noise reduction and automatic speech recognition.