FIR

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]


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)





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)



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)





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)





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.

REFERENCES

[1] S. Salivahanan, A. Vallavaraj, C. Gnanaapriya,

Digital Signal Process ing, Tata McGraw-Hill, 2000.

[2] Sonika Gupta, Aman Panghal Performance,

Performance Analysis of FIR Filter Des ign by

Using Rectangular, Hanning and Hamming

Windows Methods, International Journal of

Advanced Research in Computer Science and

Soft ware Engineering Volume 2, Issue 6, June 2012.

[3] Chonghua Li, Design and Realization of FIR Digital

Filters Based on MATLAB, IEEE 2010.

[4] Saurabh Singh Rajput, Dr. S. S. Bhadauria,

Implementat ion of FIR Filter using Efficient

Window Function and its Application in Filt ering a

Speech Signal, International Journal of Electrical,

Electronics and Mechanical Controls Volume 1, Issue

1, November 2012.

[5] IOSR Journal of Electronics and Communication

Engineering (IOSR-JECE) Volume 6, Issue 6 (Jul. -

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using Various Window Function.

[6] J.G. Proakis and D.G. Manolakis, Digital Signal

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Delhi: Prentice-Hall, 2000.

[7] Magdy T. Hanna, Design of Linear Phase FIR Filters

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CIRCUITS AND SYSTEMSI: FUNDAMENTAL

THEORY AND APPLICATIONS, VOL. 49, NO. 1,

JANUARY 2002

FIR

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