Oddly enough, court testimony for e.g. fingerprint analysis hangs on the testimony of a human expert claiming 100% certainty, rather than the error characteristics of an automated algorithm. But we DO have recorded and proven False Match and False Non-Match rates from the manufacturers, independent companies, and NIST when it comes to algorithmic techniques. This seems similar to voice comparisons, where error rates are a function of how long the sample is.
I can see fairly easily showing that there are no clear discontinuities in the hum compared to what would be expected from random splicing (though as a defense attorney I would challenge that the very people who are presenting the clip are the ones introducing a spoofable signal; biometric error rates are against RANDOM and non-adversarial presentation, spoofing detection is an entirely different beast).
However, showing uniqueness of a hum sample that is n seconds long compared to the entire continuous history of background hum would be a more rigorous analysis. I wonder if the defense team requested that given that this was a new and unproven technique.
It takes hundreds of seconds of data to see power line frequency changes on a major grid. All that synchronous rotating machinery attached to the grid has to physically change speed slightly, and there's huge inertia. Here's data for the UK national grid.[2] (This is supposed to be live, but is 2 days old.) It looks like the control systems are set up to take action at 0.1Hz error, because the frequency wanders around in that range, but as soon as it gets outside, there's a speedup or slowdown to get it back in bounds.
Claims made about short audio samples are probably bogus.
[1] https://sigport.org/sites/default/files/Information%20on%20t...
It's called archaeomagnetic dating[0]. It turns out that heated ferromagnetic materials, such as magnetite, capture the magnitude and direction of the earth's magnetic field as they cool down through the Curie temperature[1]. That allows an investigator to ascertain the direction of magnetic north the last time a likely sample was heated above the Curie point. Over time, magnetic north changes with respect to true north.
[0]https://en.wikipedia.org/wiki/Paleomagnetism
[1]https://en.wikipedia.org/wiki/Curie_temperatureIm sure the waveform wouldn't be perfectly matched from one generation area with another, but when you look at a longer period of time, say a few seconds, you wouldn't be able to refute the waveform match.
Some terms to Google for more information on that would be "synchronous detection" and "lock-in amplifier."
The method in the article talks about Fourier transform techniques, but in reality, this is a correlation problem that doesn't have to be handled in the frequency domain at all. Essentially you'd do a dot product of the contents of a sliding window from the recording against the utility's own recording of the AC power waveform. When the peak value is reached, the window offset corresponds to the best estimate of the signal's position with respect to the timeframe of the recording. This benefits tremendously from bandpass filtering, in terms of saving computation time, but doesn't strictly require it.
In real life, you'd use the STFT or something like it as the author describes, but you'd use it as a convolution filter, not to locate the frequency peak. That's kind of a red herring in an otherwise-excellent article.