[SciPy-User] Hilbert transform

Alacast alacast@gmail....
Mon Aug 29 12:38:09 CDT 2011


I'm doing some analyses on sets of real-valued time series in which I want
to know the envelope/instantaneous amplitude of each series in the set.
Consequently, I've been taking the Hilbert transform (using
scipy.signal.hilbert), then taking the absolute value of the result.

The problem is that sometimes this process is far too slow. These time
series can have on the order of 10^5 to 10^6 data points, and the sets can
have up to 128 time series. Some datasets have been taking an hour or hours
to compute on a perfectly modern computing node (1TB of RAM, plenty of
2.27Ghz cores, etc.). Is this expected behavior?

I learned that Scipy's Hilbert transform implementation uses FFT, and that
Scipy's FFT implementation can run in O(n^2) time when the number of time
points is prime. This happened in a few of my datasets, but I've now
included a check and correction for that (drop the last data point, so now
the number is even and consequently not prime). Still, I observe a good
amount of variability in run times, and they are rather long. Thoughts?

Thanks!
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