Autocorrelation (correlating a signal with itself) can be used to extract a signal from noise.
The diagram shows how the signal can be extracted from the noise:
- Random noise has a distinctive 'spike' autocorrelation function.
- A sine wave has a periodic autocorrelation function
- So the autocorrelation function of a noisy sine wave is a periodic function with a single spike which contains all the noise power.
The separation of signal from noise using autocorrelation works because the autocorrelation function of the noise is easily distinguished from that of the signal.
