Natural measurements correlate over time because dynamics persist

Evidence

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: Temperature autocorrelation reveals weather’s daily and seasonal periodicities.; Autocorrelation measures periodic self-similarity in a signal across time delays. — Eric J. Heller, Why You Hear What You Hear- An…, 369; Characteristic plot structure persists while its object is interiorized across historical stages — Fredric Jameson, Marxism and Form, 294

Related

• Temperature autocorrelation reveals weather’s daily and seasonal periodicities. (similarity 0.88)
• Autocorrelation measures periodic self-similarity in a signal across time delays. (similarity 0.85)
• Autocorrelation measures how a signal correlates with itself shifted in time (similarity 0.85)
• A finite-length burst yields a short-lived autocorrelation that vanishes beyond its duration (similarity 0.84)
• Autocorrelation averages products across all shifted pairs (similarity 0.82)
• Autocorrelation magnitude reveals how long signal features persist (similarity 0.82)
• Impulse velocity response serves as a ready-made autocorrelation (similarity 0.82)
• Autocorrelation is mathematically equivalent to the power spectrum (similarity 0.80)
• Autocorrelation discriminates echoes from genuine distinct sounds. (similarity 0.80)
• A signal’s autocorrelation is a cosine sum over its sinusoidal partials. (similarity 0.80)
• Autocorrelations are positive-coefficient cosine sums maximal at zero lag (similarity 0.78)

Broader Connections

• Autocorrelation measures periodic self-similarity in a signal across time delays. #expands (0.88) — Eric J. Heller, Why You Hear What You Hear- An…, 369