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International Journal of Computer & Communication Engineering Research (IJCCER)
Volume 2 - Issue 3 May 2014
http://ijccer.org e-ISSN: 2321-4198 p-ISSN: 2321-418X Page 130
Design Technique of Lowpass FIR filter using Various
Window Function
Aparna Tiwari, Vandana Thakre, Karuna Markam
Deptt. Of ECE,M.I.T.S. Gwalior, M.P, India
Abstract- There are various sophisticated Computer Aided Design tools are available to make the digital filter fast and power efficient. Filter design and analysis tool (FDA) is one of
the Computer Aided Design tool available with MATLAB
which enables design of the digital filter blocks faster and more
accurate Finite Impulse Response , filters are one of the
primary types of filters used in Digital S ignal Processing. For the design of Low pass FIR filters complex calculations are
required.Mathematically, by substituting the values of Pass
band, transition width, pass band ripple, stop band
attenuation, sampling frequency in any of the methods from
window method, frequency sampling method or optimal method we can get the values of filter coefficients h(n).For
removing noise or cancellation of noise we use various type of
digital filter.In this paper we propose design technique of
lowpass FIR filter using various type of window function using Hamming, Hann ,Rectangular window and Kaiser window and
will analyse these windows behaviour in higher order. Kaiser
window is the best window function in FIR filter design. Using
this window we can realize that FIR filter is simple and fast.
Keywords: FIR filter, LTI, lowpass filter, MATLAB .
I. INTRODUCTION The developments in electronic technology are taking
place at a tremendous speed. Recently, Digital Signal
Processing (DSP) is used in numerous applications such as
video compression, digital set-top box, cable modems,
digital versatile disk, portable video systems/computers,
digital audio, mult imedia and wireless communications,
digital rad io, digital still and network cameras, speech
processing, transmission systems, radar imaging, acoustic
beam formers, global positioning systems, and biomedical
signal processing. The field of DSP has always been driven
by the advances in DSP applications and in scaled Very-
Large-Scale-Integrated (VLSI) [1] technologies. In different areas digital filter design techniques are widely used. The
digital filter consist of both software and hardware
implementation. In the digital filter, the input and output
signals are digital or d iscrete time sequence. Digital filters
[3] are linear t ime invariant (LTI) systems which are
characterized by unit sample response. These filters are
portable and highly flexib le. It has minimum or neglig ible
interference noise and other effects. In storage and
maintenance digital filters are easier. Digital filters reduce
the failure time. Digital filters are categorized in two parts as
fin ite impulse response (FIR)[6] and infin ite impulse
response (IIR)[2]. In comparison to IIR filters, the FIR
filters have greater flexib ility to control the shape of their
magnitude response. According to the frequency
characteristics digital filter can be divided-lowpass,
highpass, bandpass, and bandstop. The realization of FIR
filter is non-recursive in comparison to IIR filter. Bandpass
filtering plays an important role in DSP applicat ions. It can
be used to pass the signals according to the specified
frequency passband and reject the frequency other than the
passband specification. Then the filtered signal can be
further used for the signal feature ext raction. Filtering can
also be applied to perform applications such as noise
reduction, frequency boosting, digital audio equalizing, and
digital crossover, among others.
II. FIR DIGITAL FILTER
2.1 Basic Concept of FIR filte: The basic structure of FIR
filter consists of multip liers, delay elements and adders to
create the filters output. The difference equation of N order
of the recursive digital filters (FIR) can be represented as:
Where, y (n) is the output signal, h(n) is the filter coefficients
and k is the order of the filters.
Figure.1: N-order FIR digital filter block d iagram
We can express the output signal in frequency domain by
convolution of the input signal x(n) and the impulse
response h(n). Y (n) = x (n)*h (n)
The output signal is determined as,
In differential equation, the coefficient equals to
the successive value h (n) of unit-sample response.
The system function H (z) can be expressed as:
H (z) is polynomial of . .This means that all poles are
only plotted at the origin of the Z-plane. FIR filters can be designed in different ways, for
example window method, frequency sampling method,
weighted least squares method, min imax method and
1
Aparna Tiwari, et al International Journal of Computer and Communicat ion Engineering Research [Volume 2, Issue 3 May 2014]
http://ijccer.org e-ISSN: 2321-4198 p-ISSN: 2321-418X Page 131
equiripple method. Out of these methods, the window
technique is most conventional method for designing FIR
filters. 2.2 Window function method of FIR filter design: The
basic design principles of window function are to calculate
(n) by the anti-Fourier transform based on the ideal
demanded filter frequency response The
formula of (n) is shows as
Because (n) is infin itely long, we have to deal with it
by window function to get to the unit impulse response h
(n). Now it is written as
Where w (n) is the window function. Fixed window and
adjustable window are the two categories of window
function. Blackman window, Hanning, Hamming and
rectangular window are mostly used fixed window
function. Kaiser window is a type of adjustable window
function. 2.2.1 Hanning window: The Hanning window is a raised
cosine window and can be used to reduce the side lobes
while preserving a good frequency resolution compared to
the rectangular window. The hanning window is defined as
2.2.2 Hamming window : The hamming window is, like
the Hanning window, also a raised cosine window. The
hamming window exh ibits similar characteristics to the
Hanning window but further suppress the first side lobe.
The hamming window is defined as
2.2.3 Rectangular window: The rectangular window is sometimes known as a Dirichlet window. Its ideal
frequency response is smeared out by a sinc-like
function.
2.2.4 Kaiser window: The Kaiser window with parameter
is defined as
The parameter determines the shape of the window
and thus controls the trade-off between main-lobe
width and side-lobe amplitude.
III. FIR FILTERDESIGN USING FDA TOOL
The Filter Design and Analysis (FDA) tool works with
MATLAB and the signal processing toolbox to provide a
complete environment for start to finish filter design.
The FDA tool supports many advanced techniques not
available in SP tool. FDA tool is used to design filters,
quantize filter, analyze filter, modify existing filter designs,
realize simulink models of quantized direct form FIR filters.
3.1 Filter Specifications: Where W (n) is the window
function. Fixed window, in proposed method we have
taken Blackman window, Hanning, Hamming and
rectangular window and Kaiser window .We analysed using
different orders and compared all windows behaviour in higher
order. Table 1: Filter Specificat ion
Paramaeters Values
Filter Type Lowpass
Design method FIR window(=3.2 for Kaiser window only)
Filter order 35,42,50
Cut-off frequency .4 rad/sec
IV. RESULT AND SIMULATION
From table 1 we analyzed the filter using Blackman
window by FDA tool in the MATLAB and the response of
the filter is given in figure 2,3 and 4 respectively at the order
35, 42 and 50.
Figure.2: FIR Rectangular window (N=35)
Aparna Tiwari, et al International Journal of Computer and Communicat ion Engineering Research [Volume 2, Issue 3 May 2014]
http://ijccer.org e-ISSN: 2321-4198 p-ISSN: 2321-418X Page 132
Figure.3: FIR Rectangular window (N=42)
Figure.4: FIR Rectangular window (N=50)
4.2 Hamming Window: We analyzed the filter using
Hamming window or fixed widow by FDA tool in the
MATLAB and the response of the filter is given in figure 5,
6 and 7 respectively at the order 35, 42 and 50.
Figure.5 FIR Hamming window (N=35)
Figure.6: FIR Hamming window (N=42)
Figure 7: FIR Hamming window (N=50)
Aparna Tiwari, et al International Journal of Computer and Communicat ion Engineering Research [Volume 2, Issue 3 May 2014]
http://ijccer.org e-ISSN: 2321-4198 p-ISSN: 2321-418X Page 133
4.3 Hanning Window: We analyzed the filter using Hanning window or fixed widow by FDA tool in the MATLA B and the
response of the filter is given in figure 8, 9 and 10 respectively at the order 35, 42 and 50.
Figure.8: FIR Hanning window (N=35)
Figure.9: FIR Hanning window (N=42)
Figure.10: FIR Hanning window (N=50)
Aparna Tiwari, et al International Journal of Computer and Communicat ion Engineering Research [Volume 2, Issue 3 May 2014]
http://ijccer.org e-ISSN: 2321-4198 p-ISSN: 2321-418X Page 134
4.4 Kaiser Window: We analyzed the filter using Kaiser window by FDA tool in the MATLAB and the response of the filter
is given in figure 11, 12 and 13 respectively at the order 35, 42 and 50.
Figure.11: FIR Kaiser window (N=35)
Figure.12: FIR Kaiser window (N=42)
Figure.13: FIR Kaiser window (N=50)
Aparna Tiwari, et al International Journal of Computer and Communicat ion Engineering Research [Volume 2, Issue 3 May 2014]
http://ijccer.org e-ISSN: 2321-4198 p-ISSN: 2321-418X Page 135
Table 2: Comparison between different window techniques
Window
technique
Order of
the filter
Normalised
trainsition width of
main lobe
No. of side lobes
Minimum stopband
attenuation
Rectangular
Window
35
0.0250
8 -21 db
42
0.0209 10
50 0.01764 13
Hamming
Window
35
0.09166
10
-53 db
42
0.07674
13
50 0. 06470 14
Hanning
Window
35
0.08611
9 -44 db 42
0.07209
10 50 0.006078 11
Kaiser (=3.2)
Window
35
0.06199
10 > -50db 42
0.05190
11 50 0.04375 14
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 Hann
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 except rectangular window but as rectangular
window passband gain is one and magnitude of sidelobes
doesnt considerably suprresd (stopband attenuation near
main lobe), it dont preferably used. For Kaiser window it is
genrally greater than 50 db and depends on formula -
20log(), wher is stopband ripple.
The Kaiser window g ives best result. Therefore it is most
commonly used window for FIR filter design.
V. CONCLUSION
Dig ital filter can play a major role in speech signal
processing applications such as , speech filtering, speech
enhancement, noise reduction and automatic speech
recognition. The kaiser window gives the minimum
Normalised transition width of mainlobe 0.04375 after
Rectangular window but as it has lowest stopband
attenuation cant preferably used and as Kais er window
has better s topband attenuat ion (>50 db) for filter order
50 which means this window has less transition width and
introduces more ripple.
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Digital Signal Process ing, Tata McGraw-Hill, 2000.
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[3] Chonghua Li, Design and Realization of FIR Digital
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