Side-by-side comparison
| Parameter | Butterworth | Chebyshev IIR Filter |
|---|---|---|
| Passband Response | Maximally flat — zero ripple | Type I: ripple in passband; Type II: ripple in stopband |
| Roll-off Sharpness | Moderate — gentler than Chebyshev for same order | Steeper roll-off for same filter order |
| Pole Locations | Equally spaced on a circle in s-plane | Ellipse in s-plane (closer to jΩ axis) |
| Phase Response | Smoother, more linear than Chebyshev | More nonlinear phase, especially near cutoff |
| Typical Passband Ripple | 0 dB (by definition) | 0.5 dB, 1 dB, or 3 dB (designer chooses) |
| Order Required for Same Selectivity | Higher order needed | Lower order achieves same stopband attenuation |
| MATLAB Design Function | butter(N, Wn) | cheby1(N, Rp, Wn) or cheby2(N, Rs, Wn) |
| Applications | Audio smoothing, anti-aliasing where flat response is critical | Communications IF filters, sharp channel selection |
| Sensitivity to Component Variation | Lower — poles farther from jΩ axis | Higher — poles near jΩ axis amplify deviations |
| All-pole Filter | Yes | Type I: yes; Type II: no (has zeros) |
Key differences
Butterworth places all poles on a circle of radius Ω_c in the s-plane, producing a maximally flat passband — no ripple at all from DC to cutoff. A 5th-order Butterworth achieves −40 dB at 2×Ωc. A 3rd-order Chebyshev Type I with 1 dB passband ripple achieves the same −40 dB at 2×Ωc — two orders fewer. That order reduction directly reduces computational load in real-time implementations. However, Chebyshev poles lie on an ellipse closer to the jΩ axis, making the filter more sensitive to coefficient quantization errors in fixed-point DSPs like the TMS320C54x. Butterworth is the safer default for audio paths where flat amplitude from 20 Hz to 20 kHz is non-negotiable.
When to use Butterworth
Use Butterworth when passband flatness is the primary constraint — medical instrumentation amplifiers, audio DAC reconstruction filters, and precision measurement systems where passband droop is unacceptable.
When to use Chebyshev IIR Filter
Use Chebyshev Type I when transition-band sharpness matters more than passband flatness — IF bandpass filters in AM/FM receivers, channel selection in SDR receivers using RTL2832U, or anti-aliasing before a 12-bit ADC sampling at 100 kSPS.
Recommendation
Choose Butterworth for audio and instrumentation. Choose Chebyshev when you need a sharper transition band and can accept 0.5–1 dB passband ripple. For most student projects and lab work, butter(4, Wn) in MATLAB is the safe starting point; switch to cheby1() only when the Butterworth order becomes impractically high.
Exam tip: GATE and university papers ask you to compare pole locations and state which filter has poles on a circle vs an ellipse — Butterworth is circle, Chebyshev is ellipse — and to derive the order N needed for a given stopband attenuation.
Interview tip: Interviewers at semiconductor and communications companies ask the trade-off in one sentence — say "Butterworth maximizes flatness, Chebyshev maximizes selectivity for the same order" and follow up with the MATLAB function pair.