cross-correlation
Sign in to savethumb|400px|Visual comparison of convolution, cross-correlation and [[autocorrelation. For the operations involving function , and assuming the height of is 1.0, the value of the result at 5 different points is indicated by the shaded area below each point. Also, the vertical symmetry of is the reason f*g and f \star g are identical in this example.]]
Article
24 sectionsContents
- Cross-correlation of deterministic signals
- Explanation
- Properties
- Cross-correlation of random vectors
- Definition
- Example
- Definition for complex random vectors
- Cross-correlation of stochastic processes
- Cross-correlation function
- Cross-covariance function
- Definition for wide-sense stationary stochastic process
- Cross-correlation function
- Cross-covariance function
- Normalization
- Properties
- Symmetry property
- Time delay analysis
- Zero-normalized cross-correlation (ZNCC)
- Normalized cross-correlation (NCC)
- Nonlinear systems
- See also
- References
- Further reading
- External links
thumb|400px|Visual comparison of convolution, cross-correlation and [[autocorrelation. For the operations involving function , and assuming the height of is 1.0, the value of the result at 5 different points is indicated by the shaded area below each point. Also, the vertical symmetry of is the reason f*g and f \star g are identical in this example.]]
In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recognition, single particle analysis, electron tomography, averaging, cryptanalysis, and neurophysiology. The cross-correlation is similar in nature to the convolution of two functions. In an autocorrelation, which is the cross-correlation of a signal with itself, there will always be a peak at a lag of zero, and its size will be the signal energy.