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Cross-covariance

returns the cross-covariance of two
discrete-time sequences. Cross-covariance measures the similarity between a vector
`c`

= xcov(`x`

,`y`

)`x`

and shifted (lagged) copies of a vector `y`

as
a function of the lag. If `x`

and `y`

have different
lengths, the function appends zeros to the end of the shorter vector so it has the same
length as the other.

returns the
autocovariance sequence of
`c`

= xcov(`x`

)`x`

. If `x`

is a matrix, then `c`

is a matrix whose columns contain the autocovariance and cross-covariance sequences for
all combinations of the columns of `x`

.

[1] Orfanidis, Sophocles J.
*Optimum Signal Processing: An Introduction*. 2nd Edition. New York:
McGraw-Hill, 1996.

[2] Larsen, Jan. “Correlation
Functions and Power Spectra.” November, 2009. `https://www2.imm.dtu.dk/pubdb/edoc/imm4932.pdf`