how do I interpret power density/FFT plot of a temperature-time series?

Hello,

I have a temperature-time series that I have acquired at 10kHz. The temperature varies between 50 and 56 degrees C (323 and 329 K). When I plot the FFT without normalizing it by sample length, I get the plot as attached. When I normalize it using the sample length, the Y-scale in the plot goes from 0 to 0.9.

What does this mean in terms of the original temperature data? Have I performed this incorrectly? I have also plotted this in terms of power density (periodogram) but I am not sure how to interpret the results in terms of temperature.

[dpb]

Might want to peruse

http://physics.mercer.edu/hpage/psd-tutorial/psd.html

for an extensive treatise on units of PSD. Everything said of power from a voltage measurement, say, carries over to whatever the units are of the measurement.

Of course, as the shape shows, the ability of temperature to change at a very high rate is quite limited so there's little other than a 1/f roll-off from DC. You'll have to open up the frequency scale or also go log(f) to be able to see anything of interest if there is anything to be seen and likely if there is it'll simply be reflecting the driving input if there were an external stimulus during the time of the measurement.

[v10as]

Thanks. But how do I interpret the Y-scale in the plot? The temperatures that I have in the time series are in the range of 320 K. I see a magnitude of 1200 on the FFT plot. I have also attached the power spectral density plot.

The link that you provided talks about a PSD for a mechanical oscillator. It seems a little easier to understand PSD in this example since there is force and displacement involved, that are used to calculate power dissipated. In my case, I am only providing a transient temperature set as an input. How is the periodogram/PSD inferring power dissipated, from this information?

[dpb]

It isn't power but the units are analogous to work thru with your temperature in place of the power measurement. How, precisely, as the article shows, depends on just exactly what you did in computing the spectrum.

Again, as the above also shows, there's little to interpret that I can see, anyways. What do you think you're going to accomplish here, anyway; what's the purpose behind this exercise?

[v10as]

Sorry about the late reply.

I am trying to look for differences in the PSD or FFT of two different plots. I have attached FFTs for both. What can I infer from the FFTs shown?

Answer 1

[Nitin Khola]

The fast Fourier transform (fft) is an algorithm for calculating a discrete Fourier transform of a sequence. The Fourier transform converts a time domain signal to frequency domain. The obtained output from "fft" is the discrete Fourier transform of the input. In the case you provided, the output is T(f) when the input is T(t) where (f),(t) stand for frequency and time respectively.

In general, the relative magnitudes of signal with respect to frequencies are of interest. The maximum value of "Magnitude" of the output from "fft" in MATLAB is (Length of input signal)*(Amplitude of input signal/2) as it divides the power between the negative and positive frequencies. Hence, to obtain the same maximum value from "fft" as the amplitude input time signal, the output needs to be scaled i.e. divided by the input signal length and multiplied by 2, e.g., in the following command for an input signal T, multiply T_fft by 2.

>> T_fft= abs(fft(T))/length(T);

Refer to the "fft" documentation for details and examples. For more information on fast Fourier transforms, refer to this MATLAB Answers post.