All of cam's Comments + Replies

Ok so I found time to try this out. Treating this like an audio signal makes sense, so that we can use analytical tools available in audio signal processing. The overall challenge is effectively to try and determine whether each sample is white noisey [https://en.wikipedia.org/wiki/White_noise] enough. Why? Think about what white noise is in this context. It's a pure random process. We're trying to determine if there are any particular patterns or skews to each sequence, or if the noise isn't 'white' enough. If someone put down a completely repeatable sequence, say: [0,1,0,1,0,1,0,1,0,1...] If you were to transform the range to [-1,1,-1,1...] and put it into Audacity, (try it, you can import->raw data) you'd hear a tone, (or an inaudibly short bleep in this case). Very much not random. In an FFT, we'd see a spike in this particular frequency on our spectrum. Imagine summing our first sequence with another random repeatable sequence on top: [0,1,0,1,0,1...] + [0,0,0,1,1,1,0,0...] = [0,1,0,2,1,2,0,1...] Do some tricks to normalize and rescale the data, and we'd hear two different tones. We'd now have two spikes in our FFT. Imagine just carrying this on for, say, 1000 times - then do our scaling and rounding. The FFT would be so filled out that it would look almost flat The more tones of random frequency, phase + amplitude you add, the closer and closer it comes to white noise, and therefore a perfectly random process. White noise, in theory, should be maximally flat. That means that all frequencies over the possible range have equal power. For a short sequence such as this it won't be perfectly flat, however any large skew in any direction, suggests the presence of patterns which are not random. We can use two simple spectral features to show this: Spectral Centroid (i.e the centre of mass) Spectral Flatness (i.e a measure of how flat the spectrum is) -------------------------------------------------------------------------------- Plots FFT of a pseudor