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

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 F pass of 1Hz, F stop 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 F pass of 0.7839Hz, F stop 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.