The Chebyshev filter has ripples in the PassBand, has less hardware requirements and hence costs less. The whole idea is clearly seen in the spectrum analysis-cost trade off. A bad magnitude spectrum for good cost efficiency.
The conclusion this time was interesting. The poles of both type of filters were on the right hand side of the s-plane. Which means unstable, but then why are they used as filters??
Also the ripples in the passband(number of valley and peaks) is equal to the filter's order.
Also the ripples in the passband(number of valley and peaks) is equal to the filter's order.
In the magnitude response of the Low Pass Filter, there is ripple in the pass band whereas the stop band is monotonic and there is no ripple. In the magnitude response of the High Pass, there is ripple in the stop band whereas the response is monotonic in the pass band.
ReplyDeleteIf u plot the pole zero plot for digital spectrum, u can observe that all poles lie inside the unit circle. Which means digital chebyshev filter is stable
ReplyDeleteDigital filter*
DeleteThe filter had poles inside an ellipse. Umm... So unit ellipse? ?
DeleteYou kind of answered your question.. "costs less"
ReplyDeleteChebyshev filter demonstrates that the poles lie on an ellipse in s-space centred at s = 0.
ReplyDelete