## Sampling frequency of slow phenomena to obtain PSDs

Started by 6 years ago7 replieslatest reply 6 years ago141 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

[ - ]

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

[ - ]

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.)

[ - ]
I meant 1.2 Hz.
[ - ]
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.

[ - ]

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

[ - ]

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

[ - ]