Bessel Filter Group Delay

Formula

Description

Bessel (Thomson) filters are designed for maximally flat group delay, meaning all frequency components within the passband experience the same time delay. This preserves the waveshape of transient signals and prevents pulse distortion. For a first-order section, the group delay equals the RC time constant. Bessel filters have the gentlest rolloff of all classical filter types but excel in applications where signal fidelity matters more than frequency selectivity, such as pulse measurement, medical instrumentation, and audio crossovers.

Variables

• τ — Group delay of the filter section (s)
• R — Resistance (Ω)
• C — Capacitance (F)

Practical Notes

Bessel filter rolloff is only 20 dB/decade per order initially but steepens at frequencies well above cutoff. The step response has no overshoot for orders up to about 6. Bessel filters are harder to design than Butterworth because the pole locations are not evenly distributed. Pre-computed Bessel polynomial coefficients are used for practical designs.