dsp-0.2.1: Haskell Digital Signal ProcessingSource codeContentsIndex
DSP.Covariance
Portabilityportable
Stabilityexperimental
Maintainerm.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
cxySource
:: (Ix a, Integral a, RealFloat b)
=> Array a (Complex b)y
-> Array a (Complex b)k
-> aC_xy[k]
-> Complex b

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_bSource
:: (Ix a, Integral a, RealFloat b)
=> Array a (Complex b)y
-> Array a (Complex b)k
-> aC_xy[k] / N
-> Complex b
biased cross-covariance
cxy_uSource
:: (Ix a, Integral a, RealFloat b)
=> Array a (Complex b)y
-> Array a (Complex b)k
-> aC_xy[k] / (N-k)
-> Complex b
unbiased cross-covariance
cxxSource
:: (Ix a, Integral a, RealFloat b)
=> Array a (Complex b)k
-> aC_xx[k]
-> Complex b

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_bSource
:: (Ix a, Integral a, RealFloat b)
=> Array a (Complex b)k
-> aC_xx[k] / N
-> Complex b
biased auto-covariance
cxx_uSource
:: (Ix a, Integral a, RealFloat b)
=> Array a (Complex b)k
-> aC_xx[k] / (N-k)
-> Complex b
unbiased auto-covariance
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