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, Keywords filter design.
Highlights
A filter is a device that passes certain frequency components in a signal spectrum through a system without any distortion and blocks other frequency components (Mitra, 1998)
In the design of IIR filters, a commonly used approach is called the bilinear transformation. This design begins with the transfer function of an analog filter, and a mapping from s to z plane results in a general form for an IIR filter with an arbitrary number of poles and zeros
The derivations sequel to equations 16 and 17 were used to calculate the normalized angular frequencies for the digital filters designed by Matlab which are used to determine the magnitude and phase response of the filters
Summary
A filter is a device that passes certain frequency components in a signal spectrum through a system without any distortion and blocks other frequency components (Mitra, 1998). In the design of IIR filters, a commonly used approach is called the bilinear transformation. This design begins with the transfer function of an analog filter, and a mapping from s to z plane results in a general form for an IIR filter with an arbitrary number of poles and zeros. The system response and the difference equation for this filter are (Smith, 2006):. From this expression, the output difference equation y(n) can be obtained as:. The frequency domain response function can be obtained from its z-transform (Smith, 2006):
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