Refresh - Method for cleaning noise from a measured sweep

A while back there was a thread discussing how to 
effectively clean the noise and some reflections out of the 
measurement of the response to a sweep to be used for 
impulse response extraction in the audio band.

One way is to filter the response with a narrow bandpass 
whose center frequency sweeps with it but the method 
mentioned that sounded most interesting to me was to 
modulate it down to baseband with a time varying signal, 
filter it with a fixed lowpass and then modulate it back up 
to where it was.  A link was given to a paper with more 
detail and I marked that post for future reference but it 
has slipped off my server.  If anybody knows that reference 
or cares to have any further discussion on the method I'd 
appreciate it because the time has come when I need to 
employ it.

A specific question to start with is if I just multiply the 
response with the stimulus sweep point by point have I not 
effected that time varying modulation down to baseband? 
Would the upper sideband alias down all over the place to 
make the result useless or could upsampling separate it?


Thanks,

Bob
-- 

"Things should be described as simply as possible, but no 
simpler."

                                              A. Einstein

Bob Cain wrote:
> 
> A while back there was a thread discussing how to effectively clean the 
> noise and some reflections out of the measurement of the response to a 
> sweep to be used for impulse response extraction in the audio band.
> 
> One way is to filter the response with a narrow bandpass whose center 
> frequency sweeps with it but the method mentioned that sounded most 
> interesting to me was to modulate it down to baseband with a time 
> varying signal, filter it with a fixed lowpass and then modulate it back 
> up to where it was.  A link was given to a paper with more detail and I 
> marked that post for future reference but it has slipped off my server.  
> If anybody knows that reference or cares to have any further discussion 
> on the method I'd appreciate it because the time has come when I need to 
> employ it.
> 
> A specific question to start with is if I just multiply the response 
> with the stimulus sweep point by point have I not effected that time 
> varying modulation down to baseband? Would the upper sideband alias down 
> all over the place to make the result useless or could upsampling 
> separate it?
> 
> 
> Thanks,
> 
> Bob

If you're just trying to extract the system information it isn't 
necessary to remodulate.  What _is_ necessary is to modulate it down 
with both the inphase and quadrature portions of the excitation so you 
catch a reasonable figure when you have 90 degrees of phase shift, and 
to make sure that you modulate for a sufficiently long time (hundreds or 
even the low thousands, if your system has noise).  This is essentially 
what network analyzers do, and you get all the information out that you 
need for a Bode plot.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Bob Cain <arcane@arcanemethods.com> wrote in message news:<cnk0fc0sso@enews3.newsguy.com>...
> A while back there was a thread discussing how to 
> effectively clean the noise and some reflections out of the 
> measurement of the response to a sweep to be used for 
> impulse response extraction in the audio band.
> 
> One way is to filter the response with a narrow bandpass 
> whose center frequency sweeps with it but the method 
> mentioned that sounded most interesting to me was to 
> modulate it down to baseband with a time varying signal, 
> filter it with a fixed lowpass and then modulate it back up 
> to where it was.  A link was given to a paper with more 
> detail and I marked that post for future reference but it 
> has slipped off my server.  If anybody knows that reference 
> or cares to have any further discussion on the method I'd 
> appreciate it because the time has come when I need to 
> employ it.
> 
> A specific question to start with is if I just multiply the 
> response with the stimulus sweep point by point have I not 
> effected that time varying modulation down to baseband? 
> Would the upper sideband alias down all over the place to 
> make the result useless or could upsampling separate it?
> 
> 
> Thanks,
> 
> Bob

Bob,

One way to extract the impulse response is to convolve the
contaminated chirp with the time reversed, conjugated source 
chirp. If you do this, it seems to me to be analogous to a
point by point shift to baseband.

John

John Sampson wrote:

> One way to extract the impulse response is to convolve the
> contaminated chirp with the time reversed, conjugated source 
> chirp. If you do this, it seems to me to be analogous to a
> point by point shift to baseband.

Thanks, John.  For a linear sweep I believe that yields the 
impulse response.  Problem is, if the measurement is noisy 
(my noise is highly autocorrelated since it is noise from 
the ambient acoustic environment) and that noise corrupts 
the resulting IR.  I'm looking for ways of cleaning up the 
response sweep before applying the correlation you describe 
to extract the IR.


Bob
-- 

"Things should be described as simply as possible, but no 
simpler."

                                              A. Einstein

Tim Wescott wrote:

> If you're just trying to extract the system information it isn't 
> necessary to remodulate.  What _is_ necessary is to modulate it down 
> with both the inphase and quadrature portions of the excitation so you 
> catch a reasonable figure when you have 90 degrees of phase shift, and 
> to make sure that you modulate for a sufficiently long time (hundreds or 
> even the low thousands, if your system has noise).  This is essentially 
> what network analyzers do, and you get all the information out that you 
> need for a Bode plot.

'Fraid I didn't understand that.  Given a sampled sweep and 
the sampled response, can you be more specific as to the 
operations I would perform to get a noise reduced response?


Thanks,

Bob
-- 

"Things should be described as simply as possible, but no 
simpler."

                                              A. Einstein

Bob Cain wrote:
> 
> 
> John Sampson wrote:
> 
>> One way to extract the impulse response is to convolve the
>> contaminated chirp with the time reversed, conjugated source chirp. If
>> you do this, it seems to me to be analogous to a
>> point by point shift to baseband.
> 
> 
> Thanks, John.  For a linear sweep I believe that yields the impulse
> response.  Problem is, if the measurement is noisy (my noise is highly
> autocorrelated since it is noise from the ambient acoustic environment)
> and that noise corrupts the resulting IR.  I'm looking for ways of
> cleaning up the response sweep before applying the correlation you
> describe to extract the IR.

Maybe I'm missing something. (That's been happening a lot lately) The
ambient noise is broadband, but the signal of interest and any one time
is very narrow. Consider a so-called lock-in amplifier technique. The
test signal is generated with a quadrature oscillator; one phase is the
stimulus. The return is fed to two synchronous detectors, each one
driven by a phase. The detector outputs consist of DC representing the
signal and AC due to extraneous pickup. Low-pass filters with bandwidth
consistent with the sweep speed isolate the signal. The square root of
the sum of the filter outputs' squares is the amplitude, and their arc
tangent gives the phase. More trouble than worth, perhaps, but workable.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Bob Cain wrote:
> 
> 
> Tim Wescott wrote:
> 
>> If you're just trying to extract the system information it isn't 
>> necessary to remodulate.  What _is_ necessary is to modulate it down 
>> with both the inphase and quadrature portions of the excitation so you 
>> catch a reasonable figure when you have 90 degrees of phase shift, and 
>> to make sure that you modulate for a sufficiently long time (hundreds 
>> or even the low thousands, if your system has noise).  This is 
>> essentially what network analyzers do, and you get all the information 
>> out that you need for a Bode plot.
> 
> 
> 'Fraid I didn't understand that.  Given a sampled sweep and the sampled 
> response, can you be more specific as to the operations I would perform 
> to get a noise reduced response?

Got it!  I took the Hilbert transform of my source sweep and 
multiplied the measurement by both the sweep and the 
transform, low pass filtered each of those results, 
multiplied the sweep and the transform by those filtered 
results and summed.  Voila!  Clean as a whistle.  How very cool!

I made the low pass a linear phase one so that I could just 
chop half that length off the front of the filtered result 
to get alignment for re-multiplying the quadrature sweeps.

Now to figure out how narrow I need that low pass to get rid 
of nearby reflections (measurement is a mic recording a 
speaker with some reflective objects nearby.)


Bob
-- 

"Things should be described as simply as possible, but no 
simpler."

                                              A. Einstein

Bob Cain <arcane@arcanemethods.com> wrote in message news:<cnlh9r01mh6@enews2.newsguy.com>...
> John Sampson wrote:
> 
> > One way to extract the impulse response is to convolve the
> > contaminated chirp with the time reversed, conjugated source 
> > chirp. If you do this, it seems to me to be analogous to a
> > point by point shift to baseband.
> 
> Thanks, John.  For a linear sweep I believe that yields the 
> impulse response.  Problem is, if the measurement is noisy 
> (my noise is highly autocorrelated since it is noise from 
> the ambient acoustic environment) and that noise corrupts 
> the resulting IR.  I'm looking for ways of cleaning up the 
> response sweep before applying the correlation you describe 
> to extract the IR.
> 
> 
> Bob

This may be a naive suggestion, but what if you sweep multiple
times and average the results, perhaps centering all the impulse
responses at their peaks? It also seems to me that, as suggested
earlier, a longer sweep will improve the SNR.

John

Bob Cain wrote:

> 
> Got it!  I took the Hilbert transform of my source sweep and multiplied 
> the measurement by both the sweep and the transform, low pass filtered 
> each of those results, multiplied the sweep and the transform by those 
> filtered results and summed.  Voila!  Clean as a whistle.  How very cool!
> 
When I do this for analyzing control systems I'm sourcing the sweep, so 
I can just source the quadrature component at the same time -- i.e. I 
have sin(wt) and cos(wt) available to me if I want -- but your way 
certainly works.

> I made the low pass a linear phase one so that I could just chop half 
> that length off the front of the filtered result to get alignment for 
> re-multiplying the quadrature sweeps.
> 
Why do you have to put it back together?  Are you not just getting the 
Bode plot (which you can get from your baseband results)?

> Now to figure out how narrow I need that low pass to get rid of nearby 
> reflections (measurement is a mic recording a speaker with some 
> reflective objects nearby.)
> 
I'm not sure that you _will_ be able to get rid of those reflections -- 
they're going to be changing the transfer function that you're 
measuring.  I don't know if there's any good way to distinguish between 
the part of the transfer function that results from the speaker and the 
part that results from the reflection.
> 
> Bob





-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Tim Wescott wrote:
> Bob Cain wrote:
> 
>> Got it!  I took the Hilbert transform of my source sweep and 
>> multiplied the measurement by both the sweep and the transform, low 
>> pass filtered each of those results, multiplied the sweep and the 
>> transform by those filtered results and summed.  Voila!  Clean as a 
>> whistle.  How very cool!
>>
> When I do this for analyzing control systems I'm sourcing the sweep, so 
> I can just source the quadrature component at the same time -- i.e. I 
> have sin(wt) and cos(wt) available to me if I want -- but your way 
> certainly works.

Yeah, I would have preferred it that way too but in this 
case the sweep is given as data for the program that does 
the cross correlation to extract the IR.  It regenerates the 
matched filter each time to equal the length of the 
measurement (clock mismatches between generation and 
recording are thus correctable without resampling.)

> 
>> I made the low pass a linear phase one so that I could just chop half 
>> that length off the front of the filtered result to get alignment for 
>> re-multiplying the quadrature sweeps.
>>
> Why do you have to put it back together?  Are you not just getting the 
> Bode plot (which you can get from your baseband results)?

No, I'm extracting the system IR from the sweep.

> 
>> Now to figure out how narrow I need that low pass to get rid of nearby 
>> reflections (measurement is a mic recording a speaker with some 
>> reflective objects nearby.)
>>
> I'm not sure that you _will_ be able to get rid of those reflections -- 
> they're going to be changing the transfer function that you're 
> measuring.  I don't know if there's any good way to distinguish between 
> the part of the transfer function that results from the speaker and the 
> part that results from the reflection.

That's just what I'm working on.  I see already that they 
can be considerably reduced in magnitude and bandpassed to 
low frequencies which is of some help.  The problem is 
always separating LF reflections from LF response of the SUT 
and I don't think there is a way out of that but the higher 
frequency components of the reflections do seem to be highly 
attenuated doing this.

You are right, though, when the width of the filter that 
blocks the reflections gets too short then more than noise 
and reflections are moved.  The response you are looking for 
gets smoothed too.  In my case I'm using it for system 
inversion and don't want that.  There are interesting trade 
offs doing this that I'm getting a handle on by modeling it.


Bob
-- 

"Things should be described as simply as possible, but no 
simpler."

                                              A. Einstein