Chebyshev Filters

Chebyshev filters come in two flavors: the Type-I and Type-II.

The Chebyshev Type-I Low-Pass Filter

Chebyshev Type-I filters are also all-pole filters, with poles of the normalized ($\omega _{0}$) filter located on an ellipse inside the unit circle. This arrangement of poles results in (1) a shorter transition band, and therefore a steeper roll-off compared to the Butterworth low-pass filter of the same order, (2) poorer group delay characteristics, and (3) ripples in the pass-band.