What are the distinguishing features of a Chebyshev filter?

A Chebyshev filter is characterized by its unique response within the passband, which specifically allows for ripple. This means that the gain in the passband is not uniform, enabling the filter to achieve a steeper roll-off near the cutoff frequency compared to other filter types. The acceptance of ripple allows for a more compact design, which can effectively isolate the desired frequency within the passband while still maintaining a tight transition to the stopband. This property distinguishes Chebyshev filters from other types, such as Butterworth filters, which have a smooth passband without ripple, but are less sharp in the cutoff.

The trade-off for this ability to have ripple is that the filter's phase response can become more complex compared to filters that do not allow such variations in gain. The ripple in the passband indicates that the output amplitude will not be entirely flat but will instead fluctuate within a specified range.

In contrast, a flat passband is characteristic of a Butterworth filter, which seeks to maintain a smooth response. A sharp cutoff is indeed a feature of Chebyshev filters, but it is primarily the ripple in the passband that sets them apart from filters without ripple. Providing constant gain throughout the passband is not a feature of Chebyshev filters