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Autocorrelation Function

Measure how similar a signal is to a time-shifted version of itself

20 Hz
30%

Detected Period

-- samples (-- Hz)

Original Signal x[n]

Autocorrelation R[k]

Sliding Correlation Animation

Power Spectral Density

Autocorrelation Applications

Pitch Detection: Find the fundamental frequency of speech or music by locating the first major peak after lag 0.

Periodicity Detection: Identify repeating patterns in time series data (machine vibrations, ECG, etc.).

Noise Reduction: Random noise has near-zero autocorrelation at non-zero lags, while periodic signals maintain correlation.

Wiener-Khinchin Theorem: The autocorrelation and power spectral density are Fourier transform pairs.