If an ideal low-pass filter existed, it would completely eliminate signals above the cutoff
frequency, and perfectly pass signals below the cutoff frequency. In real filters, various trade-offs
Butterworth filters are termed maximally-flat-magnitude-response filters, optimized for gain
flatness in the pass-band. the attenuation is –3 dB at the cutoff frequency. Above the cutoff
frequency the attenuation is –20 dB/decade/order. The transient response of a Butterworth filter
to a pulse input shows moderate overshoot and ringing.
Bessel filters are optimized for maximally-flat time delay (or constant-group delay). This means
that they have linear phase response and excellent transient response to a pulse input. This
comes at the expense of flatness in the pass-band and rate of rolloff. The cutoff frequency is
defined as the –3-dB point.
Chebyshev filters are designed to have ripple in the pass-band, but steeper rolloff after the
cutoff frequency. Cutoff frequency is defined as the frequency at which the response falls below
the ripple band. For a given filter order, a steeper cutoff can be achieved by allowing more
pass-band ripple. The transient response of a Chebyshev filter to a pulse input shows moreovershoot and ringing than a Butterworth filter