Indian Journal of Science and Technology

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The Design and Implementation of a Digital Infinite Impulse Response (IIR) Lowpass Butterworth Filter-a Comparison of Matlab and Bilinear Transformation Methods


Affiliations
1 Dept. of Physics, University of Jos, Jos., Nigeria
2 Dept. of Science and Technology, Kaduna Polytechnic, Nigeria
 

This research compares two IIR digital filter design and implementation methods- viz MATLAB direct method and Bilinear transformation method. Programs to design and implement Butterworth IIR lowpass digital filters were developed and executed using both methods. In the design, at Fpass of 1Hz, Fstop of 2.414 Hz, using MATLAB method the 3 dB frequency is at 1.605 Hz while using the Bilinear transformation method the 3 dB frequency is at 1.395 Hz. At Fpass of 0.7839Hz, Fstop of 2.007 Hz, using MATLAB method the 3 dB frequency is at 1.181 Hz while using the Bilinear method the 3 dB frequency is at 1.001 Hz. From the design it was observed that the Butterworth filter has maximally flat passband in its frequency response and a poor roll-off at its bandstop which is in line with predicted theory. The Butterworth filters designed using Bilinear transformation were more stable with a monotonically decreasing gain response due to its poor roll-off which may be associated to discrete component performance. The magnitude of the passband decreases as the order of the filter increases. The designs also show that higher order filters have sharper skirts and may be used in phase modulated wave (PMW) applications.

Keywords

Matlab, Bilinear Transformation Methods, Filter Design
User

  • Kwaha BJ (2007) The development of digital filtering techniques for application in continuous wave (CW) radar systems. Ph. D thesis in the postgraduate school, University of Jos, Nigeria.

  • Liman MS (1996) Design and implementation of digital filters using windows. M.Sc. thesis in the post graduate school, University of Jos, Nigeria.

  • Mitra SK (1998) Digital signal processing (A computer based Approach), New York, NY: McGraw-Hill, 2nd edn.

  • Mitra SK (2002) Digital signal processing (A computer based approach). McGraw Hill book company, New York, 3rd edn.

  • Ogubuike SC (1986) Electrical filters. B. Sc., thesis, University of Jos, Nigeria.

  • Smith JO (2006) Introduction to Digital filters. www.http://ccrma.stanford.edu/ jos/filters06/.


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  • The Design and Implementation of a Digital Infinite Impulse Response (IIR) Lowpass Butterworth Filter-a Comparison of Matlab and Bilinear Transformation Methods

Abstract Views: 585  |  PDF Views: 146

Authors

B. J. Kwaha
Dept. of Physics, University of Jos, Jos., Nigeria
E. A. Kolawole
Dept. of Physics, University of Jos, Jos., Nigeria
A. M. Batu
Dept. of Science and Technology, Kaduna Polytechnic, Nigeria

Abstract


This research compares two IIR digital filter design and implementation methods- viz MATLAB direct method and Bilinear transformation method. Programs to design and implement Butterworth IIR lowpass digital filters were developed and executed using both methods. In the design, at Fpass of 1Hz, Fstop of 2.414 Hz, using MATLAB method the 3 dB frequency is at 1.605 Hz while using the Bilinear transformation method the 3 dB frequency is at 1.395 Hz. At Fpass of 0.7839Hz, Fstop of 2.007 Hz, using MATLAB method the 3 dB frequency is at 1.181 Hz while using the Bilinear method the 3 dB frequency is at 1.001 Hz. From the design it was observed that the Butterworth filter has maximally flat passband in its frequency response and a poor roll-off at its bandstop which is in line with predicted theory. The Butterworth filters designed using Bilinear transformation were more stable with a monotonically decreasing gain response due to its poor roll-off which may be associated to discrete component performance. The magnitude of the passband decreases as the order of the filter increases. The designs also show that higher order filters have sharper skirts and may be used in phase modulated wave (PMW) applications.

Keywords


Matlab, Bilinear Transformation Methods, Filter Design

References





DOI: https://doi.org/10.17485/ijst%2F2011%2Fv4i4%2F30022