## xcorr

r = xcorr( x , y ) returns the cross-correlation of two discrete-time sequences. Cross-correlation measures the similarity between a vector x and shifted (lagged) copies of a vector y as a function of the lag. If x and y have 关于IQ Option期权平台上出金提款问题解答 different lengths, the function appends zeros to the end of the shorter vector so 关于IQ Option期权平台上出金提款问题解答 it has the same length as the other.

r = xcorr( x ) returns the autocorrelation sequence of x . If x is a matrix, then r is a matrix whose columns contain the autocorrelation and cross-correlation sequences for all combinations of the columns of x .

r = xcorr( ___ , maxlag ) limits the lag range from -maxlag to maxlag for either of the previous syntaxes.

r = xcorr( ___ , scaleopt ) also specifies a normalization option for the cross-correlation or autocorrelation. Any option other than 'none' (the default) requires x and y to have the same length.

[ r , lags ] = xcorr( ___ ) also returns the lags at which the correlations are computed.

## Examples

### Cross-Correlation of Two Vectors

Create a vector x and a vector y that is equal to x shifted by 5 elements to the right. Compute and plot the estimated cross-correlation of x and y . The largest spike occurs at the lag value when the elements of x and y match exactly (-5).

### Autocorrelation of Vector

Compute and plot the estimated autocorrelation of a vector x . The largest spike occurs at zero lag, when x matches itself exactly.

### Normalized Cross-Correlation

Compute and plot the normalized cross-correlation of vectors x and y with unity peak, and specify a maximum lag of 10 .

## Input Arguments

### x — Input array

vector | matrix | multidimensional array

Input array, specified as a vector, matrix, or multidimensional array. If x is a multidimensional array, then xcorr operates column-wise across all dimensions and returns each **关于IQ Option期权平台上出金提款问题解答** 关于IQ Option期权平台上出金提款问题解答 autocorrelation and cross-correlation as the columns of a matrix.

**Data Types:** single | double **Complex Number Support:** Yes

### y — Input array

vector

Input array, specified as a vector.

**Data Types:** single | double **Complex Number Support:** Yes

### maxlag — Maximum lag

integer scalar

Maximum lag, specified as an integer scalar. If you specify maxlag , the returned cross-correlation sequence ranges from -maxlag to maxlag . If you do not specify maxlag , the lag range equals 2*N* – 1, where *N* is the greater of the lengths of x and y .

**Data Types:** single | double

### scaleopt — Normalization option

'none' (default) | 'biased' | 'unbiased' | 'normalized' | 'coeff'

Normalization option, specified as one of the following.

'none' — Raw, unscaled cross-correlation. 'none' is the only valid option when x and y have different lengths.

'biased' — Biased estimate of the cross-correlation:

R ^ x y , biased ( m ) = 1 N R ^ x y ( m ) .

'unbiased' — Unbiased estimate of the **关于IQ Option期权平台上出金提款问题解答** cross-correlation:

R ^ x y , unbiased ( m ) = 1 N − | m | R ^ x y ( m ) .

'normalized' or 'coeff' — Normalizes the sequence so that the autocorrelations at zero lag equal 1:

R ^ x y , coeff ( m ) = 1 R ^ x x ( 0 ) R ^ y y ( 0 ) R ^ x y ( m ) .

## Output Arguments

### r — Cross-correlation or autocorrelation

vector | matrix

Cross-correlation or autocorrelation, returned as a vector or matrix.

If x is an *M* × *N* matrix, then xcorr(x) returns a (2*M* – 1) × *N* 2 matrix with the autocorrelations and cross-correlations of the columns of x . If you specify maxlag , then r has size (2 × maxlag + 1) × *N* 2 .

For example, if S has three columns, S = ( x 1 x 2 x 3 ) , then the result of R = xcorr(S) is organized as

R = ( R x 1 x 1 R x 1 x 2 R x 1 x 3 R x 2 x 1 R x 2 x 2 R x 2 x 3 R x 3 x 1 R x 3 x 2 R x 3 x 3 ) .

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