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I'm looking for a Python package or method to accurately estimate the arrival time of time signals.

A single time signal is stored inside a 1-dimensional numpy array, so every component of the array represents the value of the signal at a given timestep.

Here is an example of the signals shape:

enter image description

Setting a threeshold is not always efficient, it depends on the signal behaviour and amplitude.

I would like to find a gradient based method to identify the starting timestep. Do you have any relevant experience or suggestion?

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  • $\begingroup$ Does this have to be done in real-time? If not, there are many more options available. $\endgroup$ – Peter K.♦ Jan 29 '17 at 22:20
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    $\begingroup$ No they are data from a tsunami simulation database. Each Recording represents water elevation associated with a specific geographical point (x,y). To compare different mareograms (signals) collected in different locations, hence with different arrival times, I need to estimate their arrival time as accurately as possible. $\endgroup$ – Matteo Scarponi Jan 30 '17 at 12:33
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    $\begingroup$ Cool! Sounds like a fun project. I'll try to write an answer later (probably tomorrow), but look up CUSUM, particularly this answer. You may have to apply it to the high-pass signal (gradient signal) or you may want to look at an "energy" measure. $\endgroup$ – Peter K.♦ Jan 30 '17 at 12:39
  • $\begingroup$ I'll look at it! Seems pretty useful $\endgroup$ – Matteo Scarponi Jan 30 '17 at 17:32
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A gradient-based method is essentially a high-pass filter, if you think about it. ("gradient" being "derivative" for 1D signals, and the derivative being small for non-changing signals, and very high for high-frequency signals). And that's exactly how I implement it:

  • Signal in
  • high-pass filter
  • abs()
  • find first above threshold
  • subtract delay of filter¹

You can do so by designing a high-pass filter using scipy.signal.fir_filter_design and apply it using scipy.signal.filter.

Another popular method, which is mainly interesting if you want to do this on a live stream of samples, is doing the same within GNU Radio, where you can take the filter taps from the filter design, and put them into a readily available FIR filter. I kind of covered that in a blog post once, and you might want to read the first chapters of the GNU Radio Guided Tutorials, too.

¹: this requires your filter to have constant group delay, i.e. be linear-phase.

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As mentioned before, a high pass filter can add delays to your detector. If your filter is not linear-phase, the delay depends on the frequency of your signal. Another approach is the called Onset Detection, or a detection of a sudden burst of energy. A great paper about this is here.

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I think Marcus' technique is a good approach. However, if you want to avoid the phase-delay introduced by the high-pass filter, you could filter the signal twice. See Zero-phase Filtering. Granted you are filtering a given signal twice, but there is no added phase delay and, again, this is off-line data.

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  • $\begingroup$ You can always save your data to memory and filter it twice. So this works even in online setups, as long as your filtering operations can be done under schedule. $\endgroup$ – The Dude Oct 26 '17 at 18:22

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