"Smoothing" a Frequency Response

Hello,

Is it possible to intelligently smooth an experimentally gathered
frequency response? I have input and output time history signals, to
which I apply an in-house FFT/windowing/smoothing program to compute
the gain, phase, and coherence. I then compare the results to an
analytically generated response. On many of these runs, the higher end
of the measured frequency response is very "noisy" in all 3
components. I was wondering if it is possible to sensibly  "filter"
the magnitude & phase curves to eliminate this noise. Is there some
theoretical reason, for example, that the slope of the magnitude and
phase curves is limited somehow? I know that (for non-minimum phase
systems) that there is a certain relationship between the magnitude
and phase curves, but I don't think I can use that fact since both
curves are very noisy in the same frequency range

Thanks
Roy

On Feb 21, 6:28&#4294967295;pm, Roy <brewer....@gmail.com> wrote:
> Hello,
>
> Is it possible to intelligently smooth an experimentally gathered
> frequency response? I have input and output time history signals, to
> which I apply an in-house FFT/windowing/smoothing program to compute
> the gain, phase, and coherence. I then compare the results to an
> analytically generated response. On many of these runs, the higher end
> of the measured frequency response is very "noisy" in all 3
> components. I was wondering if it is possible to sensibly &#4294967295;"filter"
> the magnitude & phase curves to eliminate this noise. Is there some
> theoretical reason, for example, that the slope of the magnitude and
> phase curves is limited somehow? I know that (for non-minimum phase
> systems) that there is a certain relationship between the magnitude
> and phase curves, but I don't think I can use that fact since both
> curves are very noisy in the same frequency range
>
> Thanks
> Roy

You need to average the FFTs over successive runs.


Hardy

Thanks. These signals are so "noisy" that I suspect it would take many
runs to produce a "clean" signal. Is there a way to get the results
without averaging multiple runs? I'd rather have my test team spend
less time in the lab, if at all possible.

- Roy

On Feb 21, 1:13&#4294967295;am, HardySpicer <gyansor...@gmail.com> wrote:

>
> You need to average the FFTs over successive runs.
>
> Hardy

On Feb 21, 12:28&#4294967295;am, Roy <brewer....@gmail.com> wrote:
> Hello,
>
> Is it possible to intelligently smooth an experimentally gathered
> frequency response? I have input and output time history signals, to
> which I apply an in-house FFT/windowing/smoothing program to compute
> the gain, phase, and coherence. I then compare the results to an
> analytically generated response. On many of these runs, the higher end
> of the measured frequency response is very "noisy" in all 3
> components. I was wondering if it is possible to sensibly &#4294967295;"filter"
> the magnitude & phase curves to eliminate this noise. Is there some
> theoretical reason, for example, that the slope of the magnitude and
> phase curves is limited somehow? I know that (for non-minimum phase
> systems) that there is a certain relationship between the magnitude
> and phase curves, but I don't think I can use that fact since both
> curves are very noisy in the same frequency range
>
> Thanks
> Roy

There's no theoretical reason for the slope of either curve to be
limited. Think of the simple example of a pure bin-centered sinusoid,
which will look like a Kronecker delta in the magnitude output.

I believe you can get "smoother-looking" (yes, I know that's a
qualitative conclusion) results using parametric PSD-estimation
algorithms (e.g. linearly-constrained, minimum-variance or LCMV
estimation); I don't have any references handy right now.
Alternatively, the easiest way to decrease the variance in your PSD
estimates is to average multiple FFTs. You can use Welch's method of
overlapping FFTs and averaging them together to give you a nicer-
looking estimate.

Jason

>Hello,
>
>Is it possible to intelligently smooth an experimentally gathered
>frequency response? I have input and output time history signals, to
>which I apply an in-house FFT/windowing/smoothing program to compute
>the gain, phase, and coherence. I then compare the results to an
>analytically generated response. On many of these runs, the higher end
>of the measured frequency response is very "noisy" in all 3
>components. I was wondering if it is possible to sensibly  "filter"
>the magnitude & phase curves to eliminate this noise. Is there some
>theoretical reason, for example, that the slope of the magnitude and
>phase curves is limited somehow? I know that (for non-minimum phase
>systems) that there is a certain relationship between the magnitude
>and phase curves, but I don't think I can use that fact since both
>curves are very noisy in the same frequency range
>
>Thanks
>Roy

I am by no means an expert, or even very competent in dsp.  That being
said, I had a similar problem but with the lower frequencies.  If the
"noise" is confined to a frequency range, it sounds like it might be a
background spectrum that you could remove.  In my case, I was able to
significantly clean my signal by averaging over many signals (as already
suggested), and subtracting the background spectrum from any new incoming
spectrum.  I determined the background spectrum by taking a samples of just
the background initially before I started my experiment.

The way you choose your windowing in the time domain may also have some 
significant influence on your computed frequency response...

Okay, I guess the message is to do more runs. Does anyone know of any
good reference works for this? Or how to best window & average.

Thanks for all your help.

- Roy


On Feb 21, 1:02&#4294967295;pm, Sebastian Doht <seb_d...@lycos.com> wrote:
> The way you choose your windowing in the time domain may also have some
> significant influence on your computed frequency response...

Roy schrieb:
> Okay, I guess the message is to do more runs. Does anyone know of any
> good reference works for this? Or how to best window & average.
> 
> Thanks for all your help.
> 
> - Roy
> 
> 
> On Feb 21, 1:02 pm, Sebastian Doht <seb_d...@lycos.com> wrote:
>> The way you choose your windowing in the time domain may also have some
>> significant influence on your computed frequency response...
> 

Doing more runs is always a good idea, but I was refering to the effect 
of time windowing on non-periodic signals (or periodic signals without 
synchronization) in the frequency domain. So I do not know what your 
inhouse smoothing/windowing/fft does and you do not have to tell me, but 
if it is using only rectangular non-overlapping windows some of the mess 
you see might be the result from spectral leakage. But that was just a 
guess...