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 2N – 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 (2M – 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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