Group Delay
Canonical Definition
Group delay is the negative derivative of phase with respect to angular frequency:
τg = -dφ / dωIt describes how the timing of a narrow band or modulation envelope changes with frequency in a linear time-invariant system.
Plain-Language Meaning
Group delay shows which frequency regions are effectively arriving later than nearby regions. A broad smooth delay may be part of normal filtering or propagation. A narrow peak can point to resonance, cancellation, filter interaction, or a measurement-reference problem.
Total, Minimum, And Excess Group Delay
| Trace | What it contains | Why it matters |
|---|---|---|
| Total group delay | Propagation, computer/interface, DSP, filters, acoustics, and timing offset | Useful only after the reference and offset are understood |
| Minimum group delay | Lowest phase behavior associated with the measured magnitude response under the chosen analysis conditions | Provides a reference for minimum-phase behavior |
| Excess group delay | Delay beyond the minimum-phase reference | Highlights non-minimum-phase behavior, cancellations, offsets, and reflections |
Remove Bulk Delay Before Interpreting Shape
A microphone several feet from a speaker naturally sees propagation delay. A computer, interface, DSP, and file-playback path may add more. If the graph rises toward a constant value at the top of the measurement band, much of that value may be overall system delay rather than a local acoustic problem.
Use a wired or acoustic timing reference, or deliberately offset time zero, before interpreting the frequency-dependent shape.
Why Magnitude And Group Delay Often Move Together
Peaks and dips in magnitude commonly have related phase rotation and group-delay features.
- A resonance can produce a magnitude peak and delayed decay.
- A deep cancellation can produce an extreme or unstable excess group-delay feature.
- A crossover transition can produce smooth, expected group delay.
- Room or cabin reflections can create position-dependent non-minimum-phase behavior.
Do not diagnose from the group-delay graph alone. Compare magnitude, phase, impulse response, decay, and nearby positions.
No Universal Audibility Threshold
A fixed statement such as “15 ms is acceptable in bass” or “5 ms is audible in the midrange” is incomplete. Audibility depends on:
- frequency and number of cycles represented by the delay
- bandwidth and Q of the feature
- program material and transient content
- level and masking
- whether the behavior is minimum phase or excess delay
- listening position and repeatability
- the measurement method and windowing
Use thresholds, where supported, as context-specific test results—not universal pass/fail lines.
Measurement Settings That Change The Result
- Timing reference and time zero: change bulk delay and phase slope.
- Impulse window: changes the magnitude and minimum-phase reference used for analysis.
- Smoothing: smooths phase and group-delay traces and can hide narrow behavior.
- Measurement bandwidth: affects minimum-phase generation and edge behavior.
- Microphone position: changes cancellations, reflections, and excess delay.
Practical Interpretation Workflow
- Confirm the timing reference and remove or document bulk delay.
- Check magnitude response for the corresponding peak, dip, or crossover.
- Inspect wrapped or unwrapped phase.
- Generate minimum and excess traces when the measurement supports it.
- Check the impulse response and decay behavior.
- Repeat at nearby positions.
- Decide whether the feature is a filter, resonance, cancellation, reflection, or measurement artifact before changing the system.
Common Mistakes
- Reading propagation delay as enclosure or crossover delay.
- Using a universal millisecond threshold.
- Attempting to EQ a deep non-minimum-phase cancellation flat.
- Ignoring window, smoothing, and time-zero settings.
- Comparing measurements from different timing references.