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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 | | -> 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] |
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| 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 |
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| 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 |
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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 |
| :: (Ix a, Integral a, RealFloat b) | | | => Array a (Complex b) | x | | -> a | k | | -> Complex b | C_xx[k] / N | | biased auto-covariance |
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| 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 |
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| Produced by Haddock version 0.4 |
