|
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 |
|
|
cxy_u |
|
|
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 |
|
|
cxx_u |
|
|
Produced by Haddock version 0.8 |