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.

# prewhitening ?

Started by ●October 4, 2005

Reply by ●October 4, 20052005-10-04

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.

Reply by ●October 4, 20052005-10-04

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.

Reply by ●October 5, 20052005-10-05

"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