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Suppose I drive a LTI system G(z) with white noise unit variance. I
can then using various means make an attempt at identifying G(z)
(assume the white noise cannot be measured but only the output of
G(z)).

I then drive a similar system G(z) with coloured noise (say in real
life speech). I could model this for some short period of time as the
cascade (convolution) of G(z) with the colouring transfer function
(for this segment of speech) of the speech - say H(z)G(z) driven by
white noise. How can I separate the two transfer functions ie split
H(z)G(z). Is this even possible? Of course this is a deconvolution
problem but even so - how to know what dynamics is due to H and what
due to G?

Hardy

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On 12 Mar, 21:27, HardySpicer <gyansor...@gmail.com> wrote:
> Suppose I drive a LTI system G(z) with white noise unit variance. I
> can then using various means make an attempt at identifying G(z)
> (assume the white noise cannot be measured but only the output of
> G(z)).
>
> I then drive a similar system G(z) with coloured noise (say in real
> life speech). I could model this for some short period of time as the
> cascade (convolution) of G(z) with the colouring transfer function
> (for this segment of speech) of the speech - say H(z)G(z) driven by
> white noise. How can I separate the two transfer functions ie split
> H(z)G(z). Is this even possible? Of course this is a deconvolution
> problem but even so - how to know what dynamics is due to H and what
> due to G?

Consider a scenario where you measure the output of
some system, and you measure nothing.

The possible causes for that fact are

1) There is no signal driving the system
2) The system blocks any input

There is no way you can tell which is correct from
only observing the output.

Rune

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>Suppose I drive a LTI system G(z) with white noise unit variance. I
>can then using various means make an attempt at identifying G(z)
>(assume the white noise cannot be measured but only the output of
>G(z)).
>
>I then drive a similar system G(z) with coloured noise (say in real
>life speech). I could model this for some short period of time as the
>cascade (convolution) of G(z) with the colouring transfer function
>(for this segment of speech) of the speech - say H(z)G(z) driven by
>white noise. How can I separate the two transfer functions ie split
>H(z)G(z). Is this even possible? Of course this is a deconvolution
>problem but even so - how to know what dynamics is due to H and what
>due to G?
>
>Hardy
>
As H(z)G(z)=G(z)H(z), if we suppose that the output of G(z) is the input of
H(z) so you can estimate H(z) with certain factor.

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