
DSP.Covariance  Portability  portable  Stability  experimental  Maintainer  m.p.donadio@ieee.org 





Description 
This module contains routines to perform cross and autocovariance
These formulas can be found in most DSP textbooks.
In the following routines, x and y are assumed to be of the same
length.


Synopsis 

cxy :: (Ix a, Integral a, RealFloat b) => Array a (Complex b) > Array a (Complex b) > a > Complex b   cxy_b :: (Ix a, Integral a, RealFloat b) => Array a (Complex b) > Array a (Complex b) > a > Complex b   cxy_u :: (Ix a, Integral a, RealFloat b) => Array a (Complex b) > Array a (Complex b) > a > Complex b   cxx :: (Ix a, Integral a, RealFloat b) => Array a (Complex b) > a > Complex b   cxx_b :: (Ix a, Integral a, RealFloat b) => Array a (Complex b) > a > Complex b   cxx_u :: (Ix a, Integral a, RealFloat b) => Array a (Complex b) > a > Complex b 


Documentation 

cxy 
:: (Ix a, Integral a, RealFloat b)   => Array a (Complex b)  x
 > Array a (Complex b)  y
 > a  k
 > Complex b  C_xy[k]
 raw crosscovariance
We define covariance in terms of correlation.
Cxy(X,Y) = E[(X  E[X])(Y  E[Y])]
= E[XY]  E[X]E[Y]
= Rxy(X,Y)  E[X]E[Y]



cxy_b 


cxy_u 


cxx 
:: (Ix a, Integral a, RealFloat b)   => Array a (Complex b)  x
 > a  k
 > Complex b  C_xx[k]
 raw autocovariance
Cxx(X,X) = E[(X  E[X])(X  E[X])]
= E[XX]  E[X]E[X]
= Rxy(X,X)  E[X]^2



cxx_b 


cxx_u 


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