Phase

Canonical Definition

Phase describes the position of a periodic component within its cycle relative to a stated reference. In an audio system, phase response shows how that relationship changes with frequency.

Phase Angle And Time Delay

For a pure time delay τ, phase changes linearly with frequency:

Phase shift (degrees) = -360 × frequency (Hz) × delay (s)

This is why one delay value cannot be described by one universal phase angle.

Polarity Is Not Phase

Polarity inversion multiplies the waveform by -1. For a sine wave that appears as a 180-degree offset, but no time has been added. A delay produces a phase angle that changes with frequency.

Read the full polarity reference.

Wrapped And Unwrapped Phase

Many graphs display phase only between -180 and +180 degrees. When the trace crosses the display boundary it wraps to the other side. A wrap is normally a display choice, not a sudden physical event.

• Wrapped phase: easier to fit on a graph, but can hide the continuous slope.
• Unwrapped phase: preserves accumulated rotation and makes delay slope easier to see.
• Excess phase: phase behavior remaining after a minimum-phase reference or bulk delay is removed.

Why Timing Reference Matters

Propagation time, interface latency, DSP latency, and computer or soundcard delay all add phase slope. If two measurements do not share the same wired or acoustic timing reference, their phase and arrival data may not be directly comparable.

Reading Phase Through A Crossover

The useful question is not whether each driver has a “nice” phase trace by itself. The useful question is whether the two acoustic outputs have the intended magnitude and relative phase through their overlap region at the observation point.

1. Measure each driver individually from the same position and timing reference.
2. Confirm usable magnitude overlap and target acoustic slopes.
3. Compare relative phase through the crossover band.
4. Measure the normal-polarity sum.
5. Invert one driver and measure the reverse-polarity null.
6. Check nearby positions when directivity or seating coverage matters.

Measurement Quality Rules

• Trust phase only where the response has adequate level and signal-to-noise ratio.
• Record smoothing, windowing, time-zero offset, polarity, crossover state, and microphone position.
• Separate bulk delay from filter or acoustic phase before interpreting the trace.
• Do not use a noisy local jump as proof of polarity or cancellation without checking magnitude and repeatability.

Common Mistakes

• Treating every wrap as a fault.
• Comparing traces with different timing references.
• Using a polarity switch as a substitute for delay.
• Matching phase at one frequency and ignoring the rest of the overlap band.
• Assuming a flat magnitude response proves correct phase or directivity.

Related Resources

• Polarity
• Delay
• Group Delay
• Crossover Summation
• Phase Response Graphs
• Time Alignment And Acoustic Integration