Group delay is the negative derivative of a filter's phase response with respect to angular frequency: τ(ω) = −dφ/dω. It tells you, in seconds, how long each frequency component is delayed by the filter. A constant group delay means linear phase and no waveform distortion.

Why does the RC filter's group delay peak near the cutoff?

The first-order RC low-pass has τ(f) = RC / (1 + (2πf·RC)²). At f=0 the delay equals RC. As frequency rises, the denominator grows and the delay falls. There is no peak — delay decreases monotonically. If you see a peak in a higher-order IIR, that is because its phase bends faster near the cutoff.

Why is FIR group delay perfectly flat?

A symmetric (linear-phase) FIR filter has a phase response that is exactly linear in frequency, so its derivative — the group delay — is a constant equal to half the filter length in samples.

What units does this tool use for delay?

Analog filters (RC, Butterworth) output group delay in milliseconds. The FIR result is shown in samples (multiply by 1/sample-rate to get seconds).

How is the Butterworth group delay computed?

The tool uses the closed-form pole positions of an N-th order Butterworth filter normalised to the given cutoff, then sums the contribution of each pole: τ(ω) = Σ σₖ / (σₖ² + (ω−ωₖ)²) over all conjugate pole pairs.

Group Delay Helper

Select a filter type, enter its parameters, and see the group delay vs. frequency plot instantly — no server needed.

Filter Parameters

Filter Type

Cutoff Frequency (Hz)

Frequency Axis: Linear Logarithmic

Group Delay vs Frequency

Set parameters above and click Compute.

Summary

Group delay measures how much time each frequency component is delayed by a filter. A flat group delay means all frequencies arrive at the output at the same time (linear phase); a non-flat curve means the filter smears the signal in time. This tool computes and plots group delay for three common filter types: the first-order RC low-pass, the N-th order Butterworth low-pass, and a symmetric FIR with a configurable number of taps.

How it works

Choose a filter type: RC low-pass, Butterworth, or FIR linear phase.
Enter the filter parameters (cutoff frequency, filter order, tap count, sample rate).
The tool computes group delay analytically for RC/Butterworth or numerically for FIR, then plots the result.
Hover over the curve to read the exact delay at any frequency.
Use the linear/log frequency axis toggle to zoom into the region you care about.

Use cases

Verify that a Butterworth filter meets a maximum group delay spec before hardware implementation.
Compare the flat group delay of an FIR filter against the non-flat delay of an RC stage.
Check the delay at the passband edge before choosing filter order.
Teach or learn why linear-phase FIR filters preserve waveform shape while IIR filters distort it.
Quickly estimate the time delay introduced at a target frequency by a simple RC network.

Frequently Asked Questions

Last updated: 2026-06-19 · Reviewed by Nham Vu