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

This module contains routines to perform cross- and auto-covariance 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 cross-covariance 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
 :: (Ix a, Integral a, RealFloat b) => Array a (Complex b) x -> Array a (Complex b) y -> a k -> Complex b C_xy[k] / N biased cross-covariance
cxy_u
 :: (Ix a, Integral a, RealFloat b) => Array a (Complex b) x -> Array a (Complex b) y -> a k -> Complex b C_xy[k] / (N-k) unbiased cross-covariance
cxx
 :: (Ix a, Integral a, RealFloat b) => Array a (Complex b) x -> a k -> Complex b C_xx[k] raw auto-covariance Cxx(X,X) = E[(X - E[X])(X - E[X])] = E[XX] - E[X]E[X] = Rxy(X,X) - E[X]^2
cxx_b
 :: (Ix a, Integral a, RealFloat b) => Array a (Complex b) x -> a k -> Complex b C_xx[k] / N biased auto-covariance
cxx_u
 :: (Ix a, Integral a, RealFloat b) => Array a (Complex b) x -> a k -> Complex b C_xx[k] / (N-k) unbiased auto-covariance