Discriminating periodic signals from aperiodic ones I was wondering if there are any well-established or known low-dimensional descriptors (i.e. heuristics or features) for the problem of discriminating periodic 1D signals from aperiodic ones. 
My take so far: 


*

*I'm thinking there may be ways of compactly encoding the DFT spectrum of the signal if I assume that I can first detect the K most dominant frequencies in the signal.     

*Similarly, I'm wondering if there are any low-dimensional statistical descriptors of a signal's autocorrelation that somehow preserve information about it's periodicity.
 A: I think that this is actually a difficult research question. As mentioned by @cardinal, the FT suffers from major drawbacks.
If I recall, the distribution of the square module of the coefficients is a scaled $\chi^2$ with 1 degree of freedom. This might be used to test that your signal is a white noise, but rejection will not tell you that it is periodic.
Wavelets turn out to be an incredibly powerful tool to study noisy pseudo-periodic (and long memory) signals. Unfortunately they are not usually used to detect periodicity and I am not aware of simple descriptors of periodicity. I came across that paper which addresses just that question, but if you are not familiar with the wavelet theory it might be hard to read.
A: Generally it is best to detect periodicity in the frequency domain.  However, if for example there is a twelve month period and the time step is one month then at lag 12 and multiples of it you should see high correlations.  If there is no periodic components there would be no peaks at a particular lag and its multiples.  So maybe as a partial answer to your question this could possibly work.  But I don't think there is any very definitive approach. 
