Improving uncertainty of tone measurements

[Dominik.Bejma]

Hello everyone 👋 

I'm looking for improving frequency, phase and amplitude measurements of sinusoidal signal done with Extract Single Tone Information VI or Tone Measurements VI. 

1. I have constant number of points from oscilloscope, but I can change time base. And here question arises: will it be better to use shorter timebase and obtain only 2-4 periods of very high horizontal resolution, or use longer time base, and obtain about 10-100 low horizontal resolution periods (for simplification let's say there is no aliasing). 

2. Is it better to collect X waveforms, average them, and then conduct tone measurements on that averaged waveform, or maybe to conduct tone measurement on each of those X waveforms and then average results? 

Best regards 

Dominik Bejma

[NIquist]

Try a web search for "LabVIEW extract tone tutorial" or similar.  There is a lot of info out there like this thread:

What does the extract single tone vi do? - NI Community

1.  My guess is that it will do better with more horizontal resolution, but I am not an expert on this.

2.  This depends on the stability of your original signal.  I would try reading the same signal many times and seeing how much variation you get.  Then, it's still up to you to decide whether to average.  If you do average, you can also report the standard deviation and variance to cover your bases.

[altenbach]

• You have not said how many points you get.
• How often does the frequency change? Do you know anything about the expected frequency?
• Can consecutive readings be appended or are there gaps?
• Do you typically get an integer number of waves per sample?

[Dominik.Bejma]

1. Let say I have about 4k points in one buffer. I believe it doesn't really matter, because everyone have different oscilloscope, measurement card, voltmeter, whatever. This question is more general: about technical approach and measurement strategy. 

2. Let say dominant frequency is constant,  with exception for insignificant fluctuations. The main deal here are harmonics and random noise. 

3. Again: It's about approach. I have those 4000 samples. No more. Of course, if I could take 1 milion it would be better - no doubt. 😉 But if i could take 1 milion, how to further improve that measurement? By taking 10 milions samples? 😄 

4. I can "cut" the readings to end with full cycle (but of course not perfectly due to horizontal resolution).

[Henrik_Volkers · Accepted solution]

If you want to measure phase, you need two (same frequency) signals to compare.

If you have noise on the signal labviews tone detection will usually fit on two sligthly different frequencies, resulting in mag and phase errors. In case of limited number of samples and noise a longer sample time (window) usually is better, but i wouldn't go below 10 points per periode.

(also depends on sampling method, integrating sampling results in systematic decreasing magnitude measurements at lower SR per periode)

Some links to papers regarding sine fitting:

STANDARD SINE FITTING ALGORITHMS APPLIED TO BLADE TIP TIMING DATA

and very detailed (more math involved!)

https://ieeexplore.ieee.org/document/893254

Rules of thumb:

- hard sync your generator and the ADCs (DAQs) , if you exactly know the frequncy  use three parameter sine fit.

-the better method use longer integration times  (very basic rule of signal processing 😄 ) -> more points and longer window (in our case only valid if the frequency is stable!)

if you really are into phase and magnitude (ppm chasing) have a look at the involved impedances!

And if free running (not hard synced) MEMS are involved, all is lost in the phase noise of the MEMS timing 😉

EDIT: If you can configure your scope to a lower SR with decimation without filter, and generator clock (stable frequency source) and scope are synced , you can use subsampling to increase the window duration to increase accuracy with a constant number of samples.  Noise is energy in a frequency band, a sine fit over a longer window decrease the frequency band of the fit, so decrease the noise.... simply explained, need some constrains...   peek into the rabbit hole: https://en.wikipedia.org/wiki/Cram%C3%A9r%E2%80%93Rao_bound

EDIT2: This need a stable frequency and magnitude. FM or AM will spread the spectrum and you will loose accuracy with increased window length.

[Dominik.Bejma]

That's very much what I was looking for! Thank You!