Phase correlation

Definition

Phase correlation between the left and right channels is the correlation coefficient of the two zero-mean signals:

r = Σ L[n] · R[n] / √( Σ L[n]² · Σ R[n]² )

The value lies between −1 and +1:

• +1: the channels are identical apart from a level factor (mono signal);
• 0: the channels are uncorrelated (very wide stereo, two independent recordings);
• −1: the channels are identical with opposite polarity; summed to mono they cancel.

For two sine waves of the same frequency and amplitude out of phase by φ, measured over a whole number of periods, r = cos φ: 90° → 0; 180° → −1. Real-time correlation meters compute r over a moving window of a few hundred milliseconds; multiband correlation meters compute r per frequency band. The goniometer (vectorscope) shows the same data in graphic form, drawing M = (L+R) on the vertical axis and S = (L−R) on the horizontal one.

Correlation, Side/Mid ratio and mono drop are linked: for channels of equal power P_S / P_M = (1 − r) / (1 + r) and the level drop in mono is 10 · log10((1 + r) / 2) dB.

Parameters and units

• Value: dimensionless, from −1 to +1.
• Integration window: 100–300 ms in real-time meters; entire file in summary measurements.
• Reference values for a full mix: average +0.3/+0.9; brief dips toward 0 on wide effects are normal; prolonged negative values indicate a problem.
• Conversion table (channels of equal power):

Musical function

Correlation immediately flags polarity inversions, delays between microphones, over-driven wideners and synthesizers with oscillators in antiphase. A mix with positive correlation keeps its balance when played back in mono; a mix with correlation close to 0 or negative loses energy, especially in the bass and the vocal, on smartphones, Bluetooth speakers and club systems.

Practical example

• Kick microphones: kick in and kick out with opposite polarity. Summed in the center they partially cancel below 200 Hz; by temporarily panning the two microphones one left and one right, the correlation meter shows negative values. Inverting the polarity of one microphone brings the correlation back to positive and the kick's low end increases by 4–6 dB.
• Guitar with two microphones at different distances: 1 ms of delay produces φ = 180° at 500 Hz, hence cancellation at 500, 1500, 2500 Hz in the sum. Aligning the tracks by 1 ms makes the cancellation disappear.
• Full mix: r = 0.65 over the whole file → Side/Mid −6.7 dB and mono drop −0.84 dB: healthy values for a pop mix.

Common mistakes

• Reading only the average value of the whole song: a brief passage with r < 0 (a pad, a riser) stays hidden in the average.
• Assuming that a correlation close to +1 is always a good result: it also indicates a mix with no width.
• Fixing low values by making the entire mix mono instead of working on the responsible track.
• Evaluating the correlation of a duplicated mono track: it is always +1 and gives no information.
• Confusing polarity and phase: polarity inversion flips the signal at all frequencies, while a phase shift depends on frequency.

How to check it

• App analysis: Stereo correlation computed over the whole file with the correlation coefficient formula; Mono sum drop and Side / Mid (total energy) complete the diagnosis; the per-band width shows which zone the side content is concentrated in.
• By section: export the suspect sections separately (breakdowns with wide pads, risers) and analyze them in the app to see the local values.
• Real-time meters: Voxengo Correlometer (multiband), iZotope Insight, Wave Candy in vectorscope mode.
• Polarity: with the track's polarity-invert button, compare the correlation and the bass level in the two positions.