Minimum-Phase Response
Canonical Definition
A causal stable system is minimum phase when it has the minimum possible phase delay for its magnitude response and a causal stable inverse, apart from an explicitly separated pure delay. In measurements, minimum-phase behavior is assessed over a stated valid frequency region and condition rather than assigned to the entire vehicle by one cutoff frequency.
Why It Matters For EQ
In a minimum-phase region, magnitude and phase are linked. A stable inverse magnitude correction also corrects the associated minimum-phase phase response. In a non-minimum-phase region, flattening magnitude does not necessarily restore the time behavior and may demand unsafe gain.
Low-frequency regions can be non-minimum phase and higher-frequency regions can be minimum phase. The result depends on the measured system, position, bandwidth, timing, and window.
Bulk Delay Is Separate
Travel time, interface latency, and other constant delays rotate phase without changing magnitude. Remove or account for that bulk delay consistently before judging minimum and excess phase. A delayed minimum-phase system remains correctable after the delay is handled.
How To Evaluate A Region
- Capture a repeatable full-range-enough measurement with a stable timing reference.
- Keep the response above the noise floor beyond the band being evaluated.
- Document impulse windows and calibration behavior.
- Generate the minimum-phase response from the measured magnitude.
- Inspect measured, minimum, and excess phase plus excess group delay.
- Repeat at nearby positions and measure individual contributors.
Typical Correctable And Risky Cases
| Observation | Likely action | Verification |
|---|---|---|
| Broad stable peak with flat excess group delay | Consider a measured cut or minimum-phase correction | Nearby positions, headroom, decay, listening |
| Deep dip with large excess-delay feature | Investigate cancellation, reflection, placement, polarity, delay, or source summation | Individual sources and position movement |
| Constant timing offset | Correct with channel delay or time-reference handling when appropriate | Impulse, phase, crossover sum |
| Feature near noise floor or invalid window range | Do not design correction yet | Improve the measurement first |