51–60 of 159 posts
This subject has bothered me for a long time. My question to guys into acoustics was always: If the cochlea performs some kind of Fourier transform, what are the chances, that it uses sinus waves as a base for the vector-space? - if it did anything like that it could just as good use any slightly different wave-forms as a base for transformation. Stiffness and non-linearity will for sure take care that any ideal rubb…
Earlier quoted context omitted.
And phase. People always forget about the phase as if it was purely imaginary.
Ha ha, as I understand it, phase is imaginary in a Fourier transform. Complex numbers are used and the imaginary portion does indeed represent phase. I have been told that reversing the process — creating a time-based waveform — will not resemble (visually) the original due to this phase loss in the round-tripping. But then our brain never paid phase any mind so it will sound the same to our ears. (Yay, MP3!)
That being said, round-tripping works just fine, axiomatically so, until you go out of your way to discard the imaginary component.
Nit: It’s an unfortunate confusion of naming conventions, but Fourier Transform in the strictest sense implies an infinite “sampling” period, while the finite “sample” period counterpart would correspond to Fourier Series even though we colloquially refer to them interchangeably. (I had put “sampling” in quotes as they’re actually “integration period” in this context of continuous time integration, though it would be…
As the article briefly mentions, it's a tempting hypothesis that there is a relationship between the acoustic properties of human speech and the physical/neural structure of the auditory system. It's hard to get clear evidence on this but a lot of people have a hunch that there was some coevolution involved, with the ear's filter functions favoring the frequency ranges used by speech sounds.
Nit: It’s an unfortunate confusion of naming conventions, but Fourier Transform in the strictest sense implies an infinite “sampling” period, while the finite “sample” period counterpart would correspond to Fourier Series even though we colloquially refer to them interchangeably. (I had put “sampling” in quotes as they’re actually “integration period” in this context of continuous time integration, though it would be…
Yeah, it's sort of like saying the ear doesn't do "a" Fourier transform, it does a bunch of Fourier transforms on samples of data, with a varying tradeoff between temporal and frequency resolution. But most people would still say that's doing a Fourier transform. As the article briefly mentions, it's a tempting hypothesis that there is a relationship between the acoustic properties of human speech and the physical/ne…
To summarize: the ear does not do a Fourier transform, but it does do a time-localized frequency-domain transform akin to wavelets (specifically, intermediate between wavelet and Gabor transforms). It does this because the sounds processed by the ear are often localized in time. The article also describes a theory that human speech evolved to occupy an unoccupied space in frequency vs. envelope duration space. It mak…
Well from an evolutionary perspective, this would be unsurprising, considering any other forms of language would have been ill-fitted for purpose and died out. This is really just a flavor of the anthropic principle.
To summarize: the ear does not do a Fourier transform, but it does do a time-localized frequency-domain transform akin to wavelets (specifically, intermediate between wavelet and Gabor transforms). It does this because the sounds processed by the ear are often localized in time. The article also describes a theory that human speech evolved to occupy an unoccupied space in frequency vs. envelope duration space. It mak…
> At high frequencies, frequency resolution is sacrificed for temporal resolution, and vice versa at low frequencies. this is the time-frequency uncertainty principle. intuitively it can be understood by thinking about wavelength. the more stretched out the waveform is in time, the more of it you need to see in order to have a good representation of its frequency, but the more of it you see, the less precise you can…
Now I'm imagining some alien shrew with vocal-cords (or syrinx, or whatever) that runs the entire length of its body, just so that it can emit lower-frequency noises for some reason.
> A Fourier transform has no explicit temporal precision, and resembles something closer to the waveforms on the right; this is not what the filters in the cochlea look like. Perhaps the ear does someting more vaguely analogous to a discrete Fourier transforms on samples of data, which is what we do in a lot of signal processing. In signal processing, we take windowed samples, and do discrete transforms on these. The…
To summarize: the ear does not do a Fourier transform, but it does do a time-localized frequency-domain transform akin to wavelets (specifically, intermediate between wavelet and Gabor transforms). It does this because the sounds processed by the ear are often localized in time. The article also describes a theory that human speech evolved to occupy an unoccupied space in frequency vs. envelope duration space. It mak…
What would it mean for a sound to not be localized in time?
The content is generally good but I'd argue that the ear is indeed doing very Fourier-y things.