# prewhitening ?

Started by October 4, 2005
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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.

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```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.
>
>
>

But why would I want to lose correlation information ?

H.

```
```"Lars Hansen" <invalid@nospam.com> wrote in message
> 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

```