The topic of this article may not meet Wikipedia's general notability guideline. Please help to demonstrate the notability of the topic by citing reliable secondary sources that are independent of the topic and provide significant coverage of it beyond a mere trivial mention. If notability cannot be shown, the article is likely to be merged, redirected, or deleted. Find sources: "Autocorrelation technique" – news · newspapers · books · scholar · JSTOR (February 2012) (Learn how and when to remove this message)

This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. Please help improve this article by introducing more precise citations. (February 2012) (Learn how and when to remove this message)

The autocorrelation technique is a method for estimating the dominating frequency in a complex signal, as well as its variance. Specifically, it calculates the first two moments of the power spectrum, namely the mean and variance. It is also known as the pulse-pair algorithm in radar theory.

The algorithm is both computationally faster and significantly more accurate compared to the Fourier transform, since the resolution is not limited by the number of samples used.

The autocorrelation of lag 1 can be expressed using the inverse Fourier transform of the power spectrum ${\displaystyle S(\omega )}$:

${\displaystyle R(1)={\frac {1}{2\pi }}\int _{-\pi }^{\pi }S(\omega )e^{i\,\omega }d\omega .}$

If we model the power spectrum as a single frequency ${\displaystyle S(\omega )\ {\stackrel {\mathrm {def} }{=}}\ \delta (\omega -\omega _{0})}$, this becomes:

${\displaystyle R(1)={\frac {1}{2\pi }}\int _{-\pi }^{\pi }\delta (\omega -\omega _{0})e^{i\,\omega }d\omega }$

${\displaystyle R(1)={\frac {1}{2\pi }}e^{i\,\omega _{0}}}$

where it is apparent that the phase of ${\displaystyle R(1)}$ equals the signal frequency.

The mean frequency is calculated based on the autocorrelation with lag one, evaluated over a signal consisting of N samples:

${\displaystyle \omega =\angle R_{N}(1)=\tan ^{-1}{\frac {{\text{im}}\{R_{N}(1)\}}{{\text{re}}\{R_{N}(1)\}}}.}$

The spectral variance is calculated as follows:

${\displaystyle {\text{var}}\{\omega \}={\frac {2}{N}}\left(1-{\frac {|R_{N}(1)|}{R_{N}(0)}}\right).}$

• Estimation of blood velocity and turbulence in color flow imaging used in medical ultrasonography.
• Estimation of target velocity in pulse-doppler radar

• A covariance approach to spectral moment estimation^{[dead link]}, Miller et al., IEEE Transactions on Information Theory. ^{[full citation needed]}
• Doppler Radar Meteorological Observations Doppler Radar Theory.^{[full citation needed]} Autocorrelation technique described on p.2-11
• Real-Time Two-Dimensional Blood Flow Imaging Using an Autocorrelation Technique, by Chihiro Kasai, Koroku Namekawa, Akira Koyano, and Ryozo Omoto, IEEE Transactions on Sonics and Ultrasonics, Vol. SU-32, No.3, May 1985.