27 Mar 2012

Butterworth filter and Chebyshev filter – A comparison

Butterworth filter and Chebyshev filter – A comparison.

In digital signal processing, we come across digital filters which are to be designed using analog filters. From these analog filters, Butterworth and Chebyshev filters are the most popular one.



[Also read: Difference between Analog and Digital Filters]

In this post, we are going to discuss some of the important differences or more specifically comparison between the two types of filters.

Some of the important differences are as follows:

Magnitude response vs frequency curve: The magnitude response  |H(jw)| of the butterworth filter decreases with increase in frequency from 0 to infinity, while the magnitude response of the Chebyshev filter fluctuates or show ripples in the passband and stopband depending on the type of the filter.

Width of Transition band: The width of the transition band is more in Butterworth filter compared to the Chebyshev filter.

Location of the poles: The poles of a Butterworth filter lies only on a circle while that of the Chebyshev filter lies on an ellipse, which can be easily concluded on looking at the poles formula for both types of filters.

No. Of Components required for implementing the filter: The number of poles in Butterworth filter is more compared to that of the Chebyshev filter of same specifications, this means that the order of Butterworth filter is more than that of a Chebyshev filter. This fact can be used for practical implementation, since the number of components required to construct a filter of same specification can be reduced significantly.
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