Low frequency cross power spectrum. Problems with number of averages.

[rjerez]

I am using Labview 5.1 on Windows 95 and the AT-MIO-16XE-50 board.
I have been trying to get the Cross Power Spectral Density (CPSD) of two signals in the frequency range from 2.0mHz to 10 Hz with a reazonable resolution. I am not seeking for any peaks, but for the shape of the CPSD. When I acquire many sets of two-averages-CPSD, and make the final average, I get wrong result. But, when I acquire many sets of five-averages-CPSD, the final result is correct.
My question is: Why the final result (say, 100 averages), is wrong when the sets are formed by two-averages, but is correct when it is formed by a number larger than 2?

Thanks in advance.
Ricardo.

[Gerald Albertini]

Ricardo,

Measuring spectral density requires a proper anti-aliasing filtering.
Is your signal band limited ? Did you make sure the sampling frequency was respecting the Nyquist criterion ?

In order to let me help you more efficiently, could you please provide the following information :
1. Signal connections (single ended or differential ?)
2. Sampling rate
3. Block sizes and total blocks used in overall averaging
4. VIs used for computing the CPSD (and input settings for the VIs)
5. Algorithm for averaging and other computations if not using built-in VIs

Could send me your VI so that I can have a closer look and try to help you with this ? (gerald.albertini@ni.com)

Gerald

[rjerez]

Hi Gerald.
Thanks for your reply.

The informations you required are as follow:

1. All connections in differential mode (floating source)
2. sampling rate = 100 Hz.
3. Block size or frame size = 8192 points or more.
4. I am using the Dynamic Signal Analyzer.vi with the following setting:
Coupling: DC
Input config: differential
High limit = 1.0V and Low limit = -1.0V.
Hanning window.
Cross power in Vrms^2/Hz unit.
Magnitude mode and linear resolution.
The number of averages are adjusted in this VI.

Also, I am using a low-pass filter as anti-aliasing filter. The cut-off is 10 Hz.
About our signals, I think that it has a very large
band (on the order of kHz). That signals, in the time
domain, have a behavior lik
e a gaussian white noise.

If you need more informations, let me know.
Thanks again.
Ricardo.

[Gerald Albertini]

Ricardo,

I will install LabVIEW 5.1 on a test machine in order to look at this more in details.
A few comments related to your reply:
Measuring floating sources with differential input may require additional resistors to avoid amplifiers saturation, please see the following article for more info :
http://zone.ni.com/devzone/conceptd.nsf/2d17d611efb58b22862567a9006ffe76/01f147e156a1be15862568650057df15?OpenDocument#3

You also mention a lowpass filter with a cutoff frequency of 10 Hz and a sampling frequency of 100 Hz.
I simply would like to make sure we are talking about an analog filter?
If this cutoff frequency is the -3dB point, some frequency components will alias in the region of interest (DC to 50 Hz).
Depending on the
sharpness of this filter, components will be more or less attenuated in the 10 to 50 Hz.
What is the order of this filter ?
I've been personally experiencing problems while trying to measure spectral densities on a signal that was not properly protected against aliasing...that's the reason why I'm kind of insisting on this aspect.

I'll make my best to provide more info as soon as possible

Regards

Gerald

[rjerez]

Hello Gerald

I am using the BNC-2110 to make my conections and
according to the manual, this accessory already have
the resistor.

The analog lowpass filter is an old (but working fine)5489A from HP. Frequencies above the cutoff
are attenuated at 12dB/octave. I have checked it.
I don´t know the order of the filter.
I didn´t mention but my region of interest is from
1.0 to 6.0 Hz where the magnitude of the CPSD is constant (white noise). In this region, is the effect
of aliasing so high?
Just remember that is the number of averages in a block
or set that causes the wrong result. With a block with 2 averages the result is wrong but with 5 averages the
result is right. So, I think, aliasing is not the
problem.
One more infor
mation: I used the signal generation of
the board to generate a gaussian white noise very
similar to the real signal and all the conditions were
identical the experiment. The gaussian noise was generated in a range of frequencies from 50 to 2kHz.
In this simulation, no problem have occurred!!
The final result (100 averages) was identical with
50 sets 2-averaged, 20 sets 5-averaged, 10 sets
10-averaged or 100 averages directly.
In other words, our real signal has something different from the generated signal.
It is a very interesting problem, isn´t it?

Regards
Ricardo.

[Gerald Albertini]

Ricardo,

sorry it took me so long to reproduce your setup.
I now have LabVIEW 5.1 running on a Win2K machine as well as a NI6052E board connected in my PC.
According to your last email, you are not able to reproduce the problem when using the analog output of the board...Could you please describe what is connected to Channel A and to Channel B (Are these 2 signals gaussian noise like signals ?)
What is the signal source of these signals? Is it an analog or digital source ?
I must admit that I don't really see why 2 averages measurements would return bad values while 5 averages measurements would not.
Maybe you could save your signals (ChA and ChB) to a file and share those so that I can have a closer look?
Di
d you try to rebuild your own VI using cross power spectrum in order to compare with the results you get with the dynamic signal analyzer.vi ?
I will make my best to try to reproduce this problem on my system.
Best regards

Gerald

[rjerez]

Hi Gerald

The real signals come from two compensated ionization
chamber (for neutron detection)located in our research
reactor IEA-R1. The current from these chambers are
changed to volts by two Keithley 614 electrometers and
the DC is removed by analog highpass filters with cut
off of 0.001 Hz (3 dB). The AC signals are amplified
by 30, resulting in signals of about 50mV peak.
These two AC signals are then sent to the lowpass filter (the HP 5489A) and are used to obtain the
CPSD. If you take many samples of these signals, choosing one point in the time domain and ploting this in a histogram, you will get a gaussian distribution. That is, the signals are very like a white noise with a gaussian distribution.
To
morrow we will begin a new set of experiments and
I will record some signals (in the time domain) to send you. Good idea. I will work with these recorded signals
to see what it happens.

Regards
Ricardo.

[rjerez]

Hi Gerald

I am having difficulties to send you the file with the real data. The file attachment procedure is not working
fine. May I send the file by e-mail? If so, please give me your e-mail address.

The data were acquired using the dynamic signal
analyzer.vi with sample rate = 100 Hz, frame size = 8192 points and the antialiasing filter with 10 Hz cutoff. The file has 81920 data points per channel so you can make a 10 averaged CPSD.
I did the calculations for 5 blocks of 2 averages and 2 blocks of 5 averages to get the final 10 averages CPSD. The results for the mean value of the final CPSD in the range from 1.0 to 6.0 Hz were:

1)5 blocks of 2 averages: 9.7054E-6 Vrms^2/Hz
2)2 blocks of 5 averages: 8.8043E-6
Vrms^2/Hz

Regards
Ricardo.

[Gerald Albertini]

Ricardo,

My email is :
gerald.albertini@ni.com

I would be very interested in looking into these files more in detail.

Thanks!

Gerald

[rjerez]

Gerald,

Using the file I sent you, I folloowed the signals with the highlight execution and probes in many places to
see where the changes begin. I noticed that after the
windowing (I was using Hanning window) the results
depend upon the number of averages. With no windowing,
the results do not depend upon the number of averages.
I will look into this in more detail.

Regards
Ricardo.