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Marc
Guest
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 Posted:
Fri Dec 02, 2005 1:16 am Post subject:
coherence of non-stationary signals |
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Hi,
I have a theoretical question about coherence (and statistics in
general I guess. When calculating the coherence of two non-stationary
signals, what are the implications of not detrending? I am writing a
function within a biosignal processing application to estimate the
coherence of two biosignals, using the Welch periodogram method
(essentially Matlab's cohere function). I am wondering if I must
remove the mean from the prewindowed sections of the input signals for
the coherence to even be meaningful.
Is it as simple as: "I'm dealing with non-stationary signals so of
course I have to detrend" ?
Thanks,
Marc |
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Peter K.
Guest
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| Posted:
Fri Dec 02, 2005 1:16 am Post subject:
Re: coherence of non-stationary signals |
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Marc wrote:
| Quote: | I have a theoretical question about coherence (and statistics in
general I guess. When calculating the coherence of two non-stationary
signals, what are the implications of not detrending? I am writing a
function within a biosignal processing application to estimate the
coherence of two biosignals, using the Welch periodogram method
(essentially Matlab's cohere function). I am wondering if I must
remove the mean from the prewindowed sections of the input signals for
the coherence to even be meaningful.
Is it as simple as: "I'm dealing with non-stationary signals so of
course I have to detrend" ?
|
Be careful: Detrending is not the same as removing the mean.
Detrending removes a linearly changing offset from the signal.
Removing the mean removes a constant offset from the signal.
Removing the mean is generally sensible, because many algorithms assume
that you have a zero-mean signal (and fail if you don't; e.g.
autocorrelations that are triangular in shape generally don't add any
information)
Removing a trend will depend on what the signal is that you're looking
at.
If the signal's mean is changing over the time of the measurements, and
is known to change in something like a linear manner, then it's
probably a good idea to remove it by detrending.
Otherwise, you could just be adding more "noise" to the problem.
Ciao,
Peter K. |
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Marc
Guest
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| Posted:
Fri Dec 02, 2005 1:16 am Post subject:
Re: coherence of non-stationary signals |
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Hi Peter,
In the Matlab function cohere, the parameter dflag is used to select
between no detrending, linear detrending and mean removal, so I was
using that nomenclature to refer to both mean removal and detrending.
Sorry to be unclear, I guess I was asking if I should be doing either.
To estimate the coherence of two input signals, I am calculating the
cross-spectrum and the autospectrums of windowed subsections of the
input signals. In the test cases I've studied so far there seems to be
little difference between removing the mean and not. I haven't tried
linear detrending yet because it's more complicated to program in C of
course.
I'm pretty sure there are no stationarity requirements to calculating
the cross and autospectra. If I'm wrong, I fear I may have to program
the linear trend removal.
Thanks,
Marc |
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