Cross-correlation
Estimate the cross-correlation between two sequences or the autocorrelation of a single sequence
xcorr(
x,
y = NULL,
maxlag = if (is.matrix(x)) nrow(x) - 1 else max(length(x), length(y)) - 1,
scale = c("none", "biased", "unbiased", "coeff")
)x |
Input, numeric or complex vector or matrix. Must not be missing. |
y |
Input, numeric or complex vector data. If |
maxlag |
Integer scalar. Maximum correlation lag. If omitted, the
default value is |
scale |
Character string. Specifies the type of scaling applied to the correlation vector (or matrix). matched to one of:
, where |
Estimate the cross correlation R_xy(k) of vector arguments x and
y or, if y is omitted, estimate autocorrelation R_xx(k) of
vector x, for a range of lags k specified by the argument
maxlag. If x is a matrix, each column of x is correlated
with itself and every other column.
The cross-correlation estimate between vectors x and y (of
length N) for lag k is given by
N
Rxy = SUM x(i+k) . Conj(y(i))
i=1where data not provided (for example x[-1], y[N+1]) is zero. Note the
definition of cross-correlation given above. To compute a cross-correlation
consistent with the field of statistics, see xcov.
The cross-correlation estimate is calculated by a "spectral" method in which the FFT of the first vector is multiplied element-by-element with the FFT of second vector. The computational effort depends on the length N of the vectors and is independent of the number of lags requested. If you only need a few lags, the "direct sum" method may be faster.
A list containing the following variables:
array of correlation estimates
vector of correlation lags [-maxlag:maxlag]
The array of correlation estimates has one of the following forms:
Cross-correlation estimate if X and Y are vectors.
Autocorrelation estimate if is a vector and Y is omitted.
If x is a matrix, R is a matrix containing the
cross-correlation estimate of each column with every other column. Lag
varies with the first index so that R has 2 * maxlag + 1 rows
and P^2 columns where P is the number of columns in x.
Paul Kienzle, pkienzle@users.sf.net,
Asbjorn Sabo, asbjorn.sabo@broadpark.no,
Peter Lanspeary. peter.lanspeary@adelaide.edu.au.
Conversion to R by Geert van Boxtel, G.J.M.vanBoxtel@gmail.com.
xcov.
## 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). n <- 0:15 x <- 0.84^n y <- pracma::circshift(x, 5) rl <- xcorr(x, y) plot(rl$lag, rl$R, type="h") ## Compute and plot the estimated autocorrelation of a vector x. ## The largest spike occurs at zero lag, when x matches itself exactly. n <- 0:15 x <- 0.84^n rl <- xcorr(x) plot(rl$lag, rl$R, type="h") ## Compute and plot the normalized cross-correlation of vectors ## x and y with unity peak, and specify a maximum lag of 10. n <- 0:15 x <- 0.84^n y <- pracma::circshift(x, 5) rl <- xcorr(x, y, 10, 'coeff') plot(rl$lag, rl$R, type="h")
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