How to Read a Phase Plot

A phase plot shows, frequency by frequency, how far a signal is ahead of or behind a reference, in degrees. The reference is drawn as the zero line.

Three references are common: the signal sent to the speaker, an arrival time the software removes, and another speaker. The same speaker, measured in the same place, draws a different trace against each reference.

In a room, the larger audible phase error is between two speakers playing the same frequencies. Through the crossover, the target is two traces that overlap, so the relative trace sits flat on zero.

A phase trace shows nothing about level. A source 30 dB below the reference and 180 degrees out of phase lowers the sum by 0.3 dB, and the same source in phase raises the sum by 0.3 dB. Phase matters where two sources are close in level, so read a phase plot together with the magnitude.

A transfer function uses two signals: the test signal sent to the speaker, and the microphone recording. The software splits both signals into frequencies and compares the microphone with the sent signal at each frequency. The microphone level divided by the sent level is the magnitude, and the microphone phase minus the sent phase is the phase response. Magnitude and phase together describe what the path from the software to the microphone does to each frequency. The path includes the converters, the interface buffers, the speaker and the air, and the sent signal is the zero line on the phase plot.

Without a delay setting, interface latency and the flight time to the microphone show up in the phase. Each millisecond turns the phase by 360 degrees at 1 kHz, so the trace tilts and wraps round the chart.

The fix is the delay setting in the measurement software. Set to latency plus flight time, the delay lines the sent signal up with the recording, and the plot shows the speaker's own phase.

Omnissiah measures the round-trip latency from output to microphone and removes the latency from every measurement automatically. Use one interface for mic and speakers, or Clock Drift Correction where they are separate, so the latency stays the same from one speaker's measurement to the next.

Most measurement software estimates when the sound reached the microphone, removes that delay, and plots what is left: the excess phase.

Remove too little delay and the trace tilts down with frequency. Remove too much and the trace tilts up. A 0.5 ms error tilts the trace by 180 degrees at 1 kHz and can look like a fault in the speaker.

A group delay plot is the slope of the excess phase trace, in milliseconds. A 0.5 ms delay error shifts the whole group delay plot by 0.5 ms and leaves the shape alone.

Omnissiah finds the delay by Minimum Phase Error (Least Squares) or Cross Correlation Peak (GCC-PHAT), under Delay Estimation in the tuning settings. The delay offset on a snapshot steps by 0.5 ms and changes the chart only, not the device.

Subtract one speaker's phase from another's, both measured at the same seat, and the result is relative phase. Latency and the arrival-time choice cancel, provided the latency stayed the same between measurements. What remains is the difference in arrival time and the difference between the two speakers' filters.

The reference speaker sits flat on zero. In the modelled pair, the mains are 2 m from the microphone and the sub 3 m, on a 4th-order Linkwitz-Riley crossover at 80 Hz. Drawn against the mains, the sub falls on a 2.9 ms slope and reaches minus 180 degrees at 171 Hz.

Make the sub the reference and the mains rise on the same slope. The speakers and the room are unchanged, and only the flat trace has moved.

Relative phase predicts summation. Two speakers at equal level and 180 degrees apart cancel. Through this crossover, 2.9 ms between sub and mains costs 3.2 dB at the worst point.

The dip falls at 97 Hz, where the sub is 102 degrees behind the mains at close to the same level. At 171 Hz the sub is 180 degrees behind but 26 dB quieter, so the sum is only 0.4 dB under the mains alone. Read relative phase together with the two levels.

Relative phase is the view NEXUS and Omnissiah correct. Omnissiah measures each speaker at the seat, then sets per-output delay, polarity and all-pass filters on NEXUS so the speakers' traces overlap through the crossover.

In Omnissiah, Set as Reference makes a snapshot the zero line for the others. The reference changes the drawing, not the sound at the seat.

A flat trace means the signal matches the reference. A linear-phase FIR filter can make a speaker's trace sit flat on zero against the source signal. However, for a sub and mains that share a crossover, a flat trace on each speaker is neither needed for a flat sum nor enough to fix the pair's summed transfer function.

The sum depends on the timing between sub and mains. Flattening each trace leaves the timing unchanged, so a linear-phase pair 2.9 ms apart dips the same 3.2 dB as a normal pair. Aligned, the normal pair sums flat with the phase rotation left in.

The phase rotation a crossover leaves in is hard to hear. Most group delay thresholds were measured on headphones with clicks, at about 1 to 3 ms between 500 Hz and 8 kHz (Blauert and Laws, 1978). Over loudspeakers, with music, midrange phase changes were generally inaudible (Lipshitz, Pocock and Vanderkooy, 1982). The crossover also turns the mains' phase most where the mains are quiet: at 40 Hz the mains lead by 273 degrees and sit 24.6 dB down.

Flattening the rotation has a cost. A linear-phase FIR filter delays the signal by half the filter's length, about 19 ms at an 80 Hz crossover. The filter's response also starts before the transient it corrects, as pre-ringing, and whether that pre-ringing is audible is still argued.

In an anechoic chamber, a speaker reaches the microphone by one path. In a room, each speaker reaches the seat by several paths, and the phase at the microphone is the sum of those arrivals. Move your head and the phase relationships between the arrivals change, so a trace flattened at the microphone holds at the microphone only.

Two speakers sharing the crossover are the case to fix. Delaying the mains by 2.9 ms removes the dip in the figure, for 2.9 ms of latency and no pre-ringing. NEXUS aligns speakers this way, with per-output delay, polarity and all-pass filters.