Forums

prewhitening ?

Started by Henrietta Denoue October 4, 2005

Could someone please explaing to me what prewhitening
of a time series does ? Or prewhitening the autocorrelation
and finding the minimum phase signal from this ?

Thanks

H.

whitening of a time series changes the power spectrum of the time series 
such that it is flat (in theory) and any two samples of the whitened time 
series are uncorrelated.



Lars Hansen wrote:
> whitening of a time series changes the power spectrum of the time series > such that it is flat (in theory) and any two samples of the whitened time > series are uncorrelated. > > >
Thanks Lars for the answer. But why would I want to lose correlation information ? H.
"Lars Hansen" <invalid@nospam.com> wrote in message
news:43428bfc$0$78287$157c6196@dreader1.cybercity.dk...
> whitening of a time series changes the power spectrum of the time series > such that it is flat (in theory) and any two samples of the whitened time > series are uncorrelated. > > >
If the original time-series can be modelled as white noise passing through a stable filter F(z) then by passing the time series through 1/F(z) we get back to a white noise sequence. This is more complicated if we have the same as above and then have additive uncorrelated noise (white or otherwise).Then we get a spectral factor as the colouring transfer function instead of F(z) but the basic idea is the same.ie suppose u(k) is white and is uncorrleated with v(k) - anotehr white noise sequence. Then y(k)=F(z)u(k) +v(k) wnd the spectrum of y is phiyy(z) = FF* X power of u + power of v where * denotes conjugate. We can then factorise the power spectrum] phiyy(z)= EE* where E is the spectral factor and the colouring transfer function in fact. If we use 1/E as a whitening filter for y(k) we arrive at a third white noise sequence called the innovations. McC