narrow band (notch?) filters at a range of frequencies

On Mar 1, 4:15 am, Rune Allnor <all...@tele.ntnu.no> wrote:
> On 1 Mar, 00:43, wbs <cssm...@gmail.com> wrote:
>
>
>
> > On Feb 29, 12:26 pm, Rune Allnor <all...@tele.ntnu.no> wrote:
> > > > 2) if this is entirely nonsensical, what is a more standard way of
> > > > finding frequency-specific differences between two signals, and then
> > > > generating a third signal that is a frequency-dependent difference of
> > > > one signal from another?
>
> > > The cross spectrum is one approach to test. Mind you, it
> > > basically detects the frequency bands where both the two
> > > signals have large energy. You want to identify where one
> > > signal is large and the other is small. That might require
> > > some tweaking, which might not be worth the effort.
>
> > right, so i first looked at the cross spectrum of the two signals, and
> > then didn't really know what to do with that.  while this may not be
> > 'worth the effort' i wonder if you can help me figure out how i might
> > actually use the cross-PSD to get at this issue.
>
> A *very* peliminary, naive approach (not to mention untested!)
> would be to first compute the energy normalized autospetcra:
>
> pxx(f) = Pxx(f)/Px
> pyy(f) = Pyy(f)/Py
>
> where Px means 'Pxx(f) integrated over f'. Then compute the
> cross spectrum cxy(f) with the same normalization - I wouldn't
> be surprised if this would look something like
>
> cxy(f)^2 = Cxy(f)^2/sqrt(Px*Py)
>
> This, all of a sudden, looks very similar to measuring the
> coherence between x and y. Which, in turn, *might* suggest
> that fitting a filter to the coherence spectrum between x
> and y might help you in your task.
>
> Just keep in mind that I post this on an 'early' saturday
> morning following a late friday night, long before I got
> any hint of breakfast. If you still take the chance to
> follow up on my dubious hunches, you might want to check
> out
>
> Bendat & Piersol: "Random Data"
>
> Rune

yes, signal coherence... this is a good lead, i think.  however, when
i do plot the coherence of the two signals, i am not entirely sure how
to interpret the results... i mean, clearly, places where the
coherence is very low are places i should think about setting bandpass
filters... problem is, i do not know how to define "very low" since
the range of the coherence plot is really only between 0 and 5e-5.  i
suppose i could start by setting bandpass filters at the local minima
in the coherence function.  comments on this idea?

thanks for this lead.  i was thinking about coherence in looking at
the cross spectral density, but hadn't specifically tried this out.

bryan

On 3 Mar, 20:22, wbsm...@gmail.com wrote:
> On Mar 1, 4:15 am, Rune Allnor <all...@tele.ntnu.no> wrote:
>
>
>
>
>
> > On 1 Mar, 00:43, wbs <cssm...@gmail.com> wrote:
>
> > > On Feb 29, 12:26 pm, Rune Allnor <all...@tele.ntnu.no> wrote:
> > > > > 2) if this is entirely nonsensical, what is a more standard way of
> > > > > finding frequency-specific differences between two signals, and then
> > > > > generating a third signal that is a frequency-dependent difference of
> > > > > one signal from another?
>
> > > > The cross spectrum is one approach to test. Mind you, it
> > > > basically detects the frequency bands where both the two
> > > > signals have large energy. You want to identify where one
> > > > signal is large and the other is small. That might require
> > > > some tweaking, which might not be worth the effort.
>
> > > right, so i first looked at the cross spectrum of the two signals, and
> > > then didn't really know what to do with that. &#4294967295;while this may not be
> > > 'worth the effort' i wonder if you can help me figure out how i might
> > > actually use the cross-PSD to get at this issue.
>
> > A *very* peliminary, naive approach (not to mention untested!)
> > would be to first compute the energy normalized autospetcra:
>
> > pxx(f) = Pxx(f)/Px
> > pyy(f) = Pyy(f)/Py
>
> > where Px means 'Pxx(f) integrated over f'. Then compute the
> > cross spectrum cxy(f) with the same normalization - I wouldn't
> > be surprised if this would look something like
>
> > cxy(f)^2 = Cxy(f)^2/sqrt(Px*Py)
>
> > This, all of a sudden, looks very similar to measuring the
> > coherence between x and y. Which, in turn, *might* suggest
> > that fitting a filter to the coherence spectrum between x
> > and y might help you in your task.
>
> > Just keep in mind that I post this on an 'early' saturday
> > morning following a late friday night, long before I got
> > any hint of breakfast. If you still take the chance to
> > follow up on my dubious hunches, you might want to check
> > out
>
> > Bendat & Piersol: "Random Data"
>
> > Rune
>
> yes, signal coherence... this is a good lead, i think. &#4294967295;however, when
> i do plot the coherence of the two signals, i am not entirely sure how
> to interpret the results... i mean, clearly, places where the
> coherence is very low are places i should think about setting bandpass
> filters...

That was the idea, yes...

> problem is, i do not know how to define "very low" since
> the range of the coherence plot is really only between 0 and 5e-5.

Ouch! Very low numbers. Wouldn't trust them at all. Either the
numerics has bugs or the general idea is flawed. I would like
to see coherence numbers in the range 0.1-1 before proceeding.

>&#4294967295;i
> suppose i could start by setting bandpass filters at the local minima
> in the coherence function. &#4294967295;comments on this idea?

Bail out! Unless you can find (and fix!) blunders and/or flaws.

> thanks for this lead. &#4294967295;i was thinking about coherence in looking at
> the cross spectral density, but hadn't specifically tried this out.

Rune

On Mar 3, 11:32 am, Rune Allnor <all...@tele.ntnu.no> wrote:

> Ouch! Very low numbers. Wouldn't trust them at all. Either the
> numerics has bugs or the general idea is flawed. I would like
> to see coherence numbers in the range 0.1-1 before proceeding.

or maybe the signals just have very low coherence?  i am pretty sure
the algorithm is working (i am using the matlab 'mscohere' function,
which returns an array of ones if i measure the coherence of one
signal with itself).  and actually, there is a high value (nearly 1)
for the lowest frequency values of my two signals.  but when i get
above anything near about 0.5 kHz (my sampling frequency is 44.1 kHz),
the values decrease to the aforementioned range.

bryan

On 3 Mar, 21:41, wbsm...@gmail.com wrote:
> On Mar 3, 11:32 am, Rune Allnor <all...@tele.ntnu.no> wrote:
>
> > Ouch! Very low numbers. Wouldn't trust them at all. Either the
> > numerics has bugs or the general idea is flawed. I would like
> > to see coherence numbers in the range 0.1-1 before proceeding.
>
> or maybe the signals just have very low coherence? &#4294967295;i am pretty sure
> the algorithm is working (i am using the matlab 'mscohere' function,
> which returns an array of ones if i measure the coherence of one
> signal with itself).

That doesn't mean too much. I don't think the Mathworks have
been all out wrong in the past, but they have a long history
of doing very simple things in very awkward ways.

>&#4294967295;and actually, there is a high value (nearly 1)
> for the lowest frequency values of my two signals. &#4294967295;but when i get
> above anything near about 0.5 kHz (my sampling frequency is 44.1 kHz),
> the values decrease to the aforementioned range.

Maybe my idea about using cross spectra and coherence functions
was flawed in the first place.

Rune