What are the methods through which we can quantify the randomness or complexity in a given signal. I know spectral flatness measure (geometric to arithmetic means) is one way to do it, but what are other common techniques?

  • $\begingroup$ One way is to quantize your signal and compress it. For example, set samples above/below the mean to 1/0. The compression ratio becomes the randomness measure. $\endgroup$ – John Jan 29 '14 at 9:55
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    $\begingroup$ What do you mean by quantifying randomness? A particular time series is either deterministic or it isn't. Spectral flatness wouldn't have anything to do with whether a signal is stochastic; I can generate a perfectly deterministic signal that has a flat power spectrum. I'm also not sure what you mean by "complexity." Sounds like you're getting at the amount of entropy in your signal, which would be related to its information content. $\endgroup$ – Jason R Jan 29 '14 at 13:13

There are two different concepts:

If you think as your signal as a single random variable $X$ that is emitting values, then what you want is to calculate the Entropy of the random variable


If you are considering the entire random signal or stochastic process, then you have to estimate the autocorrelation function. The most random signal possible is White noise, in which every sample of the signal is not correlated with any other except itself.



For a quantized or digital signal, you can get a upper bound on an estimate of information complexity or randomness by attempting to compress the data and/or the data's spectrum using a large variety of compression algorithms.


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