Performance Analysis Of High Pass FIR Filter Using Rectangular And Kaiser Window Technique

Performance Analysis Of High Pass FIR Filter Using Rectangular And Kaiser Window

Technique

1. Neetu Singh*, Sheetal Sahu**, Nikhil Agrawal***, Pro. Pranay kumar****, Smriti Baxla*****

2. *, ** ,***BE scholar, ****Assistant professor,*****M Tech Sholar

*, **,***,****,***** Department of Electrical and Electronics Engineering Institute Of Technology Korba Chhattisgarh, (India)

*Singh [email protected],**sheetal [email protected],***[email protected], ****praney- [email protected],*****smriti [email protected]

Performance Analysis of High Pass FIR Filter Using Rectangular and Kaiser Window

Technique

Neetu Singh, Sheetal Sahu, Nikhil Agrawal, Pro. Pranay Kumar and Smriti Baxla

*, ** BE scholar, ***Assistant professor,****M Tech Sholar

*, ** Department of Electrical and Electronics Engineering

***Department of Electrical and Electronics Engineering Institute Of Technology Korba Chhattisgarh, (India)

*Singh [email protected],**sheetal [email protected],***[email protected],****smriti [email protected]

ABSTRACT

In this paper a high pass FIR filter has been presented using windowing method based on Rectangular and Kaiser Window technique. The magnitude response is demonstrated for different design method at particular cut-off frequency and different filter order.

Keywords

-

Visual images, sound waves, speech of human voice, Electric voltage and current etc.

speech signal Processing seismic data processing bio medical signal processor audio comparison

financial signal processing electric guitar

economic forecasting

sound reinforcementmobilephones electrocardiogram(ECG)

electroencephalogram (EEG) Phonocardiogram(PCG).

2. FIRFILTER

A filter which has finite number of none zero terms in their impulse response is called FIR filter. This filter is also called as non recursive filter as does not have any feedback (i.e., all zeros terms present in their transfer function).

Properties of FIR filter

Phase distortion is not introduced in FIR filter have exact linear phase.

FIR filter are simple to design and provide BIBO (bounded input bounded output) stability.

They can be realized efficiently in hard ware.

The filter start-up transient has finite duration.

Response of the FIR filter depends only the present and past input sample.

The FIR high pass filter is designed using FDA tool of MATLAB.magnitude, phase and frequency response are presented with same order for each window technique are namely rectangular and Kaiser Window.

3. PARAMETER SPECIFICATION

Parameter for designing both the filter is given below- Order of the filter 9

Sampling frequency 19000

Cut-off frequency 1900

4. RECTANGULAR WINDOW

The weighting equation for rectangular window is given by-

The spectrum of ) can be obtained by taking Fourier transform of Eq.-

Substituting n=m-(M-1)/2 and replacing m by n, we get

=

The transition width of the main lobe is approximately 4π/M .The first side lobe will be 13dB down the peak of the main lobe and the rolloff will be at 20 dB per decade.

The magnitude response of the FIR high pass filter using rectangular window is given below-

Fig.-1-Magnitude response of FIR high pass filter using rectangular window.

The phase response of FIR high pass filter using rectangular window is given below-

Fig-2 phase response of the high pass FIR filter using rectangular window.

The magnitude and phase response of FIR high pass filter using rectangular window is given below-

Fig-3 magnitude and phase response of the FIR high pass filter using rectangular window.

Fig-4 filter coefficient of high pass FIR filters using rectangular window.

5. KAISER WINDOW

In a Kaiser window, the side lobe level can be controlled with respect to the main lobe peak by varying a parameter ,α .the

Wk (n) =

The filter coefficient of FIR high pass filter using Kaiser Window is given by-

Where an independent variable determined by Kaiser the parameter β isisexpressed by-

β =α [1 – (- ]

Magnitude response of FIR High Pass filter using Kaiser Window is given below

Fig-5Magnitude response of FIR High Pass filter using Kaiser Window

Phase response of FIR High Pass filter using Kaiser Window is given below is-

Fig-6Phase response of FIR High Pass filters using Kaiser Window.

The magnitude and phase response of the FIR high pass filter

Fig.-7The magnitude and phase response of the FIR high pass filter using Kaiser Window.

The filter coefficient of FIR high pass filter using Kaiser Window is given by-

Fig.-8filter coefficient of the FIR high pass filter using Kaiser Window.

6. COMPARISON OF MAGNITUDE

Frequen cy in (KHz)

Magnitu de of rectangul ar window in (dB).

Magnitu de of Kaiser window in (dB).

1 -20.87 -20

2 -5.3359 -5

3 0.5191 0.41002

4 1.6031 1.4792

5 0.3439 0.2806

6 -0.0651 -0.07605

7 0.9282 0.84315

8 1.0563 0.9774

9 0.1869 0.1744

7. PHASE COMPARISON CHART

Frequency in (kHz)

Phase of rectangular window in (dB)

Phase of Kaiser window in (dB)

1 -3.0601 -3.0637

2 -4.549 -4.577

3 -6.036 -6.0594

4 -7.5366 -7.5452

5 -9.019 -9.0328

6 -10.5066 -

10.5161

7 -12.011 -

12.0149

8 -13.5024 -

13.4921

9 -14.959 -

14.9900

8. FILTER COEFFICIENTS

Filter coefficien t h(n)

Rectangula r window

Kaiser windo w

h(0) 0.0720 0.0673

h(1) 0.0572 0.0548

h(2) 0.0001 0.0001

h(3) -0.1335 -0.1319

h(4) -0.6483 -0.6444

h(5) 0.6483 0.6444

h(6) o.1335 0.1319

h(7) -0.0001 -0.0001

h(8) -0.0572 -0.0548

h(9) -0.0720 -0.0673

9. CONCLUSION

This paper briefly describes the two techniques namely Rectangular and Kaiser Window used to design High Pass FIR filter. The availability of well defined equation for calculating window coefficient has made this method is more preferable.

Both filters are designed with same parameter. Here we concluded that the Kaiser window is best technique for designing of FIR filter which has β(adjustment for overshoot reduction &transition) that allows adjustment of the

10. REFERENCES

[1]Digital signal processing, by S Salivahanan & C Gnanapriya Tata McGraw Hill,page no. 445-458

[2]Digital signal processing, by sanjay k mitra.

[3]Digital signal processing by shilpa Ampte.

[4]. Yadwinder Kumar,Er.Gurpreet singh walia ,

“performance analysis of FIR Digital High pass filters “ IJERA vol.3 issue 2 march- april 2013 .

[5].Prof. Gopal S Gawande, “Dr. K.B Khan Chandani and T.P Marode,” performance analysis of FIR Digital filter design technique”IJSSR Vol.2,January 2012.

[6].Saurabh Singh, Dr. S . S. Bhadauria, implementation of FIR filter using efficient window function and its Application in filtering aSpeech signal”, IJEEMC, Vol.1, 1 November 2012.

[7]A Nagoor Kani ,”Digital Signal Processing”McGraw Hill Education ,Second Edition.

11. AUTHORS

Pranay Kumar Rahireceived the Bachelors of Technology degree in Electronics &Telecommunication Engineering from Government Engineering College, Guru Gasidas University, Bilaspur, Chhattisgarh, Indiain 2004,Working as a Assistant professor in electrical and electronic department of institute of technology korba since 2008 and pursuing Masters of Engineering in Electronics and Communication Engineering from National Institute of Technical Teacher’s Training & Research, Punjab University, Chandigarh, India.The author has published research paper in 13 international journal & 1national conference.

sheetal sahu perusing bachelor of engineering in electrical and electronics engineering in 6^th semester, from Institute of Technology Korba, Chhattisgarh Swami Vivekananda Technical University, Chhattisgarh, India.

Neetu singhperusing bachelor of engineering in electrical and electronics engineering in 6^th semester, from Institute of Technology Korba, Chhattisgarh Swami

Smriti Baxla received the Bachelors of Engineering in Electrical and Electronics Engineering from Institute Of Technology, Korba in the year 2014 ,Chhattisgarh ,India Now persuing Masters of Technology in Power Systems Engineering from Technorates Institute of Technology, Bhopal Madhya Pradesh.

Nikhil agrawal perusing bachelor of engineering in electrical and electronics engineering in 6^th semester, from Institute of Technology Korba, Chhattisgarh Swami Vivekananda Technical University, Chhattisgarh, India