Autocorrelation discriminates echoes from genuine distinct sounds.

Evidence

This works so well that tiny signals can be rescued from a lot of noise, as seen in figure 4.13. A pure noise signal and its autocorrelation are shown at the bottom. A noisy signal with a smooth periodic signal embedded appears at the top. The combined signal looks as ragged as the one at the bottom, which is pure noise. However, computing the autocorrelation reveals the hidden signal (top right). — Eric J. Heller, Why You Hear What You Hear- An…, 432 (#expands, via linked claim)

Autocorrelation is a check for repetition or self-similarity. Does the signal, which might look quite unruly, tend in fact to repeat patterns at regular intervals? For example, if there is a large positive fluctuation in s(t) at some time t, does there tend to be another a time τ later? Or, is it anticorrelated at time τ: most often s(t + τ) has the opposite sign as does s(t). The product s(t)s(t + τ) would be most often negative and 〈s(r)s(t + τ)〉 would be negative for that value of the time delay τ. If s(t) and s(t + τ) are uncorrelated, so that s(t)s(t + τ) is as likely positive as negative, the average and thus c(τ) will be zero at time τ. — Eric J. Heller, Why You Hear What You Hear- An…, 369 (#expands, via linked claim)

Categorization

• XREF: connects to: Echo interference creates sinusoidal power fluctuations that average to zero; Whether echoes constructively add in Fourier analysis depends on wavelength relative to echo timing.; Time-delayed sound self-addition imposes spectral notches via autocorrelation (+3 more)

Related

• Autocorrelation measures periodic self-similarity in a signal across time delays. (similarity 0.93)
• Tiny periodic signals can be recovered from heavy noise via autocorrelation (similarity 0.90)
• Time-delayed sound self-addition imposes spectral notches via autocorrelation (similarity 0.89)
• A finite-length burst yields a short-lived autocorrelation that vanishes beyond its duration (similarity 0.89)
• A signal’s autocorrelation is a cosine sum over its sinusoidal partials. (similarity 0.86)
• Detection can be modeled as cross-correlation of the signal template with actual activity (similarity 0.86)
• Impulse velocity response serves as a ready-made autocorrelation (similarity 0.85)
• Autocorrelation reveals a signal’s fundamental periodicity through periodic peaks. (similarity 0.84)
• Autocorrelation is mathematically equivalent to the power spectrum (similarity 0.84)
• Autocorrelation measures how a signal correlates with itself shifted in time (similarity 0.82)
• Whether echoes constructively add in Fourier analysis depends on wavelength relative to echo timing. (similarity 0.82)
• Autocorrelation averages products across all shifted pairs (similarity 0.82)
• Autocorrelation, proposed in 1951, remains essential to pitch perception theory (similarity 0.81)
• Autocorrelation nearly perfectly predicts perceived residue pitch across a range of tone series. (similarity 0.81)
• Most real sounds have autocorrelations that decay over time. (similarity 0.81)

Broader Connections

• Tiny periodic signals can be recovered from heavy noise via autocorrelation #expands (0.90) — Eric J. Heller, Why You Hear What You Hear- An…, 432
• Autocorrelation measures periodic self-similarity in a signal across time delays. #expands (0.85) — Eric J. Heller, Why You Hear What You Hear- An…, 369