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When measuring echolocation clicks, there are multiple ways to make some measures of amplitude, for example peak-to-peak, RMS or energy flux density (EFD). Peak-to-peak and RMS are simple, however, I am trying to measure energy flux density which is regularly used in studies of impulsive noise and also echolocators (useful because the mammalian ear acts roughly as an energy detector that integrates intensity over a time window). The actual EFD equation is pretty simple – it’s just $EDF = RMS_{dB} + 10\log(T)$ where $RMS_{dB}$ is the RMS amplitude in dB re 1 µPa and $T$ is the time in seconds.

My question is how do we measure $T$ for a click i.e. what convention should be used to find the start and end of an echolocation click and what are the signal processing approaches to achieve this? If it’s any help, I am studying harbour porpoise clicks but would be interested in other echolocation clicks/calls if methods differ between species.

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    $\begingroup$ Hi @macster110 the tag 'nbhf 'isn't very informative - could you please replace it with the full form? The Meta discussion on tags here bioacoustics.meta.stackexchange.com/q/42/131 may be of relevance. Please do chime in. $\endgroup$
    – Thejasvi
    Jul 6, 2022 at 10:34
  • $\begingroup$ Good point - done $\endgroup$
    – user213
    Jul 6, 2022 at 10:37

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For transients, the problem is the same for both computing RMS and EFD: What duration should we compute the RMS pressure over or integrate EFD over? Importantly, however, the RMS measure is highly sensitive to the chosen window and the EFD is not: If you have a click with a duration x and you by mistake compute RMS over a duration 2x around the click, then the RMS value is halved (-6 dB), whereas the EFD will be exactly the same as long as SNR is good. So the short answer is that any method that catches the dominant cycles of a click with the highest pressure will provide a robust estimation of EFD whereas the RMS estimation is inherently dodgy. If one must compute RMS for a click/transient, I like the D-duration approach (-10 dB duration of click envelope) because it is quite insensitive to noise (provided that SNR is better than 10 dB obviously), whereas the 90%/95%/99.5% of energy approach requires that one first defines a window that constitutes the 100%..

In the past, some noise polluters tried selling bungy cords by the meter by insisting on using RMS of the WHOLE noise transient including reverb which inherently lead to low RMS levels that are unlikely to exceed levels for concern and hence facilitate continued operation of the noise source. I tried to expose that problem is this paper.

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  • $\begingroup$ Great answer, thanks! $\endgroup$
    – user213
    Jul 7, 2022 at 7:55
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I'm recalling from memory so - the answer is likely to be a bit vague - apologies in advance.

One method is form a smoothed envelope of the signal and find the left-right borders set by the peak -10 dB. This was suggested in another answer by @Marinebioacoustics Aarhus Univ link here with code.

Another method I remember learning about at the SNAK course and recollect is to square the signal and run a cumulative sum over its length. The click/call duration is defined as the Xth percentile interval of the cumulative energy (X is typically 95-99 %ile). However, this method requires that a fairly narrow part of the click/call is already chosen.

The last method I've seen across papers is to just define the start/stop of a call as the portion which is Y dB above the background noise. The call is typically mean smoothed, or a running RMS is taken before the thresholding is applied.

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