Filter

Passband Behavior

Stopband Behavior

Roll-off Sharpness

Phase Response

Typical Use Case

Butterworth

Flat (no ripples)

Smooth decay

Moderate

Nonlinear

General-purpose filtering with minimal distortion in amplitude.

Elliptic

Ripple allowed

Ripple allowed

Steepest for given order

Nonlinear

When very sharp cutoff is needed despite ripple in both bands.

Bessel

Flat

Gentle decay

Very gradual

Nearly linear

Preserving waveform shape and timing (time-domain analyses).

Chebyshev Type I

Ripple allowed

Flat

Steeper than Butterworth

Nonlinear

Applications needing sharper cutoff with acceptable passband ripple.

Chebyshev Type II

Flat

Ripple allowed

Steeper than Butterworth

Nonlinear

Cases where flat passband is critical, but stopband ripple is acceptable.