Side-by-side comparison
| Parameter | Butterworth | Chebyshev Filter |
|---|---|---|
| Passband response | Maximally flat; no ripple (0 dB ripple by definition) | Equiripple; ripple of 0.5 dB, 1 dB, or 3 dB selectable |
| Roll-off steepness | Moderate; −20n dB/decade for nth order | Steeper than Butterworth for same order and ripple |
| Phase response | Better (more linear phase) | Worse; more nonlinear phase, more group delay variation |
| Transient / step response | No overshoot in step response | Exhibits ringing and overshoot due to poles near jω axis |
| Pole locations | Poles equally spaced on left-half s-plane semicircle | Poles on an ellipse in the left-half s-plane |
| Order needed for same stopband attenuation | Higher order required | Lower order for same −40 dB stopband attenuation |
| Complexity for same performance | More stages needed | Fewer stages; saves components |
| Frequency normalisation | −3 dB point exactly at ωc | −3 dB point beyond ωc for Type I; ripple edge is at ωc |
| Typical application | Audio amplifiers, anti-aliasing, any phase-sensitive path | Communications channel filters, IF filters, data modems |
| Design tables | Butterworth polynomial tables, standard | Chebyshev polynomial tables; ripple parameter ε |
Key differences
A Butterworth filter has all its poles on a semicircle in the s-plane, producing maximally flat magnitude response — no ripple anywhere in the passband. The same-order Chebyshev pushes its poles toward the jω axis, trading equiripple passband behaviour for a sharper transition band. A 5th-order Chebyshev with 1 dB ripple achieves the same stopband attenuation at 2ωc as a 7th-order Butterworth, saving two filter stages. However, Chebyshev filters ring on step inputs due to high-Q poles, making them unsuitable for time-domain pulse applications. For GATE, know that Chebyshev provides steeper roll-off at the cost of passband ripple and poorer phase linearity.
When to use Butterworth
Use a Butterworth filter when passband flatness and phase linearity are critical — for example, an anti-aliasing filter before a 24-bit audio ADC where any passband ripple directly degrades the dynamic range of the recording.
When to use Chebyshev Filter
Use a Chebyshev filter when the sharpest possible transition band is needed with a minimum number of poles — for example, a 5th-order Chebyshev IF filter centred at 10.7 MHz in an FM receiver to reject adjacent channel interference.
Recommendation
For audio and precision measurement, always choose Butterworth — its flat passband preserves signal integrity. For communications filters where adjacent-channel rejection matters more than passband flatness, choose Chebyshev. Never use Chebyshev where pulse fidelity matters; the ringing will corrupt the waveform.
Exam tip: GATE and university exams ask you to compare the pole locations on the s-plane for both filters and to state which provides maximally flat response — Butterworth — versus equiripple — Chebyshev; write this with the s-plane diagram for full marks.
Interview tip: Interviewers at DSP and communications companies ask you to explain why a Chebyshev filter requires a lower order than Butterworth for the same stopband specification, and to name the trade-off — passband ripple and poorer phase linearity.