Chebyshev filters have steeper roll-off and more passband/stopband ripples than
Butterworth filters. Chebyshev filters minimize the error between idealized and
actual filter characteristic over the range but with ripples in passband. There
is a defnite ZERO at -1, number of poles gives the ordef of filter. Magnitude
spectrum is equiripple in passband and monotonic in stop band.
We
observed that as we increase the order of filter, the ripples in passband
reduce and we get more idealized characteristics. As all poles were inside
the unit circle, the filter designed was stable.
Chebyshev filter has ripple in its response while Butterworth does not
ReplyDeleteThe ripples in passband of Chebyshev-1 filters can prove as a disadvantage as it introduces differences in gain for the passband signal.
ReplyDeletePoles are inside the unit circle thus filters are stable(HPF and LPF)
ReplyDeleteThe magnitude response is monotonic in stop band, i.e. flat without ripples, and equiripple in pass band, i.e. ripples have equal magnitude.
ReplyDeleteThe transition period for Chebyshev filter is less than that of butterworth filter.
ReplyDeleteChebyshev is preferred over Butterworth as the order of the filter is smaller for the same filter specifications so hardware requirement is less
ReplyDeleteA lower order means less hardware(delay blocks) required which lowers cost. The trade off is with quality.
ReplyDeleteIt requires less components
ReplyDeleteThe minimum order of Chebyshev filter is 2.
ReplyDelete