I thought from the title that it goes into the mathematics. Unfortunately all the article says w.r.t math is a hand-wavy explanation of autocorrelation. But it was an interesting story about the life of Auto-Tune's creator.
edit/tidbit: he told me that the interview process for hiring new developers goes like this: all the questions are straight out of K&R's C Programming Language, you have to get all of them correct, and so far only one programmer has :P
He's obviously referring to himself.
Seriously though, I’m tired of folks doing stupid counterproductive interviews and then parading them as a good thing.
That is dramatic hand-waving, but it does help convey to non-programmers how dramatic an improvement the right algorithm can implement.
It's true what the article says that pitch tracking was considered a difficult "holy grail" in 1995. I attended a talk about pitch tracking at Interval in 1996 by somebody whose name I don't remember any more. The speaker made the point that pitch is a perceptual -- not a mathematical -- concept, and it was hard but possible to do it in real time on a typical PC at the time (i.e. 90 MHZ IBM ThinkPad 760C). But he had done it, and everyone seemed impressed by his demo! ;)
The article mentioned formant analysis. Maybe that's related to cepstral analysis, which is another way of tracking the pitch and formants of voice, and has its own cool nomenclature of secret code words. "Cepstral liftering" is basically two FFT's followed by an inverse FFT.
If you take the complex FFT of a voice signal, the formants show up as two or three large "hills" in the spectrum, but the pitch manifests as higher frequency repeating furrows in the hills. (Which you want to filter out so you can analyze just the formants, or synthesize a different pitch into them (i.e. auto-tune), so you need to know the frequency of the change in the spectrum magnitude over time: another FFT!)
http://www.phon.ucl.ac.uk/courses/spsci/matlab/lect10_files/...
So you take a second FFT of the log of the first FFT, to get a "reverse spectrum" or "cepstrum" in the "quefrency" domain. The fundamental pitch shows up as one big spike in the cepstrum (with smaller spikes for its harmonics). Just "lifter" out the pitch spikes, then perform an inverse FFT to get back to the smooth low frequency formant hills with the high frequency pitch furrows removed.
I'm sure there's a lot of "special sauce" in getting the math tweaked and tuned right so it actually sounds good and runs fast.
https://stackoverflow.com/questions/4583950/cepstral-analysi...
The patent seems to be about autocorrelation, which is something different than cepstral analysis, but maybe they could be used together to get even better results.
I don't know but would love to learn what the trade-offs and limitations the two techniques have.
https://en.wikipedia.org/wiki/Cepstrum
>The name "cepstrum" was derived by reversing the first four letters of "spectrum". Operations on cepstra are labelled quefrency analysis (aka quefrency alanysis), liftering, or cepstral analysis.
https://surveillance7.sciencesconf.org/conference/surveillan...
"The original application was to the detection of echoes in seismic signals, where it was shown to be greatly superior to the autocorrelation function, because it was insensitive to the colour of the signal."