After Butterworth Filter design, the other type of IIR filter,Analog and then Digital Chebyshev filters were designed on Scilab. Here, Chebyshev-1 filter was designed with ripple in pass band and no ripple in stop band. On putting similar parameters as that of Butterworth filter for the same type, the order of Chebyshev filter is lower. There are ripples in pass band and the poles lie on an ellipse. The mapping of poles is one-to-one from s to z-plane. Here, the number of ripple peaks in the pass band is equal to the order of the filter. Both Butterworth and Chebyshev filters are Analog filters,hence their Digital filter frequency responses are similar to their analog ones. For IIR filters, stability is not guaranteed.
Its hardware implementation would be easier as compared to that of Butterworth.
ReplyDeleteIt can be implemented using difference equations.
Deleteits better than butterworth
ReplyDeleteIt involves less computation as the order is low.
DeleteChebyshev 1 has been implemented.
ReplyDeleteYes. You can refer to MATLAB's documentation for a better understanding of these filters.
DeleteChebyshev filters are used to separate one band of frequencies from another
ReplyDeleteYes.
DeleteIt has ripples in either of the bands.
ReplyDeleteTrue.
DeleteChebyshev 2 has ripples in stop band
ReplyDeleteFor some applications they can be used.
DeleteThis type of filter is named after Pafnuty Chebyshev because its mathematical characteristics are derived from Chebyshev polynomials
ReplyDeleteYes. He has also worked on Analog filter design.
DeleteChebyshev 1 filters have difference in gain for the passband signals.
ReplyDeleteThey are less preferred for critical applications.
DeleteTrue.
ReplyDeleteThanks.
ReplyDelete