Coherence and Correlation

audiotoolbox includes functions for complex-valued correlation analysis, useful for binaural and narrowband signal analysis.

Complex Correlation Coefficient

Use cmplx_corr to compute the complex correlation coefficient between two signals. The magnitude describes similarity, and the phase reflects relative phase differences.

import audiotoolbox as audio
import numpy as np

sig = audio.Signal(n_channels=2, duration=1, fs=48000)
sig.ch[0].add_tone(500)
sig.ch[1].add_tone(500, start_phase=np.pi / 4)

corr = audio.cmplx_corr(sig.ch[0], sig.ch[1])
print(corr)

Complex Cross-Correlation Over Time

For time-varying analysis, use cmplx_crosscorr with a sliding window. This is useful when phase or level relations change over time.

import audiotoolbox as audio

sig = audio.Signal(n_channels=2, duration=2, fs=48000).add_noise('white')

# Example: 20 ms analysis window
cc = audio.cmplx_crosscorr(sig.ch[0], sig.ch[1], win_len=20e-3)
print(cc.shape)

Binaural Difference Extraction

For narrowband signals, extract_binaural_differences provides instantaneous phase difference (IPD) and envelope difference between channels based on the analytic signal representation.

import audiotoolbox as audio

sig = audio.Signal(n_channels=2, duration=1, fs=48000)
sig.ch[0].add_tone(1000)
sig.ch[1].add_tone(1000, start_phase=0.3)

ipd, ild = audio.extract_binaural_differences(sig)

Notes

• These methods are most meaningful for narrowband or band-limited signals.

• For broadband stimuli, analyze in subbands (for example with a filterbank) before interpreting phase/coherence metrics.