Random number generator (Part 2)

Part 1, 2, 3

Here is a noisy signal sampled at 100 kHz with an Arduino UNO. The signal has 8 bits of resolution and the divider bridge of the final amplifying stage has been set so that the ADC range matches (without exceeding) the input signal range. Here is the illustration of a vector of 1024 data points sampled from the noise generator.

noise

You may want to download these data in order to perform your own analysis, and I would be more than happy to publish your own results.

Firstly, let’s look at the distribution of data points versus their mean value. To do so, we compute the probability mass function:

pmf

This result is typical from thermal noise. The distribution of the number of data points from each bin looks like a Gaussian distribution. Starting from there it is possible to apply envelope modelers in order to get an overall picture of the distribution. Running an Hilbert transform might overwhelm our arduino UNO so I applied a simplified algorithm which gives pretty good results.

envelope

Now we know that we are really measuring what we expect. Let see if this signal is not contaminated by other signals… To do so, we apply a FFT in order to detect the possible presence of signals characterized by individualized frequencies (and possibly their harmonics) having significant strength (signal to noise ratio). Next is the frequency spectrum from the test signal:

fft

Well, at first glance, there is nothing special to say about it. Is there something near 8 kHz ? Running this test on multiple vectors of data does not confirm this hypothesis. Running the test on extra large vectors of data would bring us to some sort of flat spectrum.

An other interesting analysis tool is the Phase Portrait. Here is a plot of the phase portrait applied to the test data. The spot is centered on the 0;0 coordinate and no repeated trend line shows up from the plot, meaning that we are dealing with real white noise.

phase_portrait

Here and there are very good examples of phase portraits applied to clean and noisy signals.

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