Sampling frequency of slow phenomena to obtain PSDs

Started by alejo_latd 5 years ago7 replieslatest reply 5 years ago130 views

Hello all, this is my first post.

In my current project I need to obtain PSDs of temperature noise from thermocouples submerged in water at 17 ºC, in this conditions the thermocouple response time is τ =7,3 s,  cutoff frequency is fc=0.022 Hz. I would like to know what is the appropriate sampling frequencies range (to avoiding aliasing and having a good resolution in the range of this phenomenon)

What kind of aspects should I take into account when I acquire the data?

I know the response of a thermocouple can be approximate to a first order system response, but I have obtained rare PSDs with some kind of resonances as you can see: temperature noise PSD

Thank you in advance!

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Reply by kjhJanuary 17, 2019

The noise you see at about 12 Hz might be from something other than the thermocouple.

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Reply by Joe_WestJanuary 17, 2019

I don't see anything at the 12 Hz noted by kjh. As I read the frequency scale, the first "peak" is at 1.2 Hz. (The center of the plot is at 10^0 Hz, which is to say 1 Hz, not 10 Hz.)

I also see secondary peaks at roughly 2.4 Hz and 3.6 Hz. These look reminiscent of what one sees when plotting |sin(x)/x| on a log-log scale. Might these "peaks" be simply artifacts of the sampling process?

Regarding the original question from alejo_latd regarding sampling frequency, depending on what you are hoping to achieve, almost anything greater than 4x or 5x the 0.022 Hz "corner frequency" of the thermocouple would seem to me to be adequate. 

Note that digitizing oscilloscopes generally sample at rates that are 4x to 5x the scope bandwidth. (This is greatly simplified from the actual sampling rate algorithms used in scope designs, but is good enough for a starting point.)

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Reply by kjhJanuary 17, 2019
I meant 1.2 Hz.
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Reply by alejo_latdJanuary 17, 2019
Hello Joe_West,

I think those resonances are result of aliasing, but i'm not sure. In literature, thermocouples' APSDs are like a first order systems response's APSD, so those resonances are not expected to me.

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Reply by Rick LyonsJanuary 17, 2019

Hello alejo_latd. Regarding your spectral plot, what does it represent? In different words, that plot is the spectrum of what time-domain signal?

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Reply by alejo_latdJanuary 17, 2019

Hello Rick Lyons, I registered the small temperature fluctuations of a thermocouple around the mean value of 17 ºC during 91 minutes. the channel setup in the data logger was: 

Sampling frequency = 50000 Hz
Downsample ratio divider = 40   
Filtered at 3 Hz (Bessel filter 8th order)

register final sampling frequency  = 1250 Hz

So these plots are the same APSD with different downsample ratio in order to get a good resolution around 0.01 - 1 Hz

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Reply by Rick LyonsJanuary 17, 2019

Hi alejo_latd. You know what is the answer to my question but you didn't tell me what is the answer to my question. The information you provided assumes I know the terminology and processing of this mysterious thing you call a "data logger". But of course I know nothing about the signals you're dealing with or what your data logger is doing. For example, you mentioned an 8th-order Bessel filter. I don't even now if that filter is an analog filter or a digital filter.

I generally support the reply that Joe_West gave to you. The only suggestion that I can give (in total ignorance of your thermocouple's output signal and total ignorance of your data logger's processing) you alejo_latd is:

If the filtered (analog lowpass anti-alias filtered to attenuate unwanted high-frequency noise) information-carrying analog signal applied to some A/D converter's input has a one-sided (positive frequencies only) bandwidth of B Hz, then the sample rate of the A/D converter should be, say, three to four times B samples/second (that is, a sample rate of 3B -to- 4B Hz).

Then again, if the analog anti-alias lowpass filter does NOT reduce unwanted noise as well as you desire, then your A/D converter should have a sample rate of, say, 10 times B so that you can use a digital lowpass filter to further reduce unwanted noise in the digital output signal from the A/D converter. Of course I'm just "talkin' off the top of my head" here.

Looking again at your PSD spectral plot, that plot looks like it *MIGHT* be the spectrum of the output of a lowpass filter whose cutoff frequency is roughly 0.4 Hz while the input to the filter is a signal containing noise over the frequency range of roughly zero Hz –to- 7 Hz. But that's just a guess on my part because I still don't know for sure what that PSD plot represents.

Anyway alejo_latd, the more information you can supply to the folks here, better chance someone here can give you a solid, valid, answer to your sample rate question.