Mixed-Phase Correction

Canonical Definition

Mixed-phase correction uses a filter whose response contains both minimum-phase and non-minimum-phase components to pursue a stated magnitude and time-domain target. A valid design is constrained by causality, stability, finite filter length, latency, headroom, measurement uncertainty, source and position variability, and the invertibility of the measured system.

Separate The Correction Jobs

1. Minimum-phase magnitude correction: correct stable response features whose magnitude and phase are linked.
2. Bulk timing: align channel or path delay separately.
3. Excess-phase shaping: address a measured all-pass, crossover, or time-domain target with a constrained filter.
4. Spatial compromise: choose which positions and listeners the correction represents.

Do not ask one inverse filter to repair routing, polarity, clipping, damaged drivers, unsafe crossover choices, or a deep spatial cancellation.

Why The Mathematical Inverse Is Not The Final Filter

• zeros or deep nulls may require unbounded gain
• the inverse may be noncausal until delayed
• finite taps truncate the desired response
• measurement noise and reflections may be inverted
• one-position behavior may not hold nearby
• the target may exceed amplifier, driver, converter, or protection limits

Regularization, gain limits, frequency limits, spatial weighting, smoothing, and time-window choices make the filter implementable and safer—but also change the theoretical inverse.

Causality And Latency

A correction that requires energy before the triggering input is noncausal. Shift it later to make it causal, reduce the requested excess-phase correction, or accept a different compromise. The shift becomes system latency and must be included in channel timing and user-interface behavior.

Design And Verification Workflow

1. Fix routing, polarity, crossover protection, gain structure, and obvious physical problems.
2. Capture repeatable individual and combined measurements at the intended positions.
3. Separate bulk delay, minimum phase, and excess phase.
4. Define the target, correction band, gain limits, spatial weights, tap count, phase target, and latency budget.
5. Generate the filter and inspect peak gain, impulse energy, predicted headroom, and causality.
6. Export to the real device with the correct sample rate and coefficient format.
7. Measure the result independently rather than trusting prediction alone.

Pass / Warning / Fail

Related Resources

• Minimum-Phase Response
• Excess-Phase Response
• Automated Room Correction
• FIR, IIR, And Room Correction