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| DSP.Covariance | | Portability | portable | | Stability | experimental | | Maintainer | m.p.donadio@ieee.org |
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| 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.
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| Synopsis |
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| 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 |
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| Documentation |
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| cxy |
| :: (Ix a, Integral a, RealFloat b) | | | => Array a (Complex b) | x
| | -> Array a (Complex b) | y
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| | -> 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]
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| cxy_b |
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| cxy_u |
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| 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
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| cxx_b |
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| cxx_u |
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| Produced by Haddock version 0.8 |
