man I need to finally learn what a Fourier transform is
humble plug
https://dsego.github.io/demystifying-fourier/
How the cochlea computes (2024)
91–100 of 159 posts
Re: How the cochlea computes (2024)
#92Why is there no box diagram for cochlea "between wavelet and Gabor" ?
Would look still too much like wavelet.
Re: How the cochlea computes (2024)
#93Earlier quoted context omitted.
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!)
I'm glad someone picked up on my dumb joke :), I was getting worried. That being said, round-tripping works just fine, axiomatically so, until you go out of your way to discard the imaginary component.
Even more complex and reflectively imaginative than the Fourier Transform is the mighty Cepstrum!
https://en.wikipedia.org/wiki/Cepstrum
It’s literally a "backwards spectrum", and the authors in 1963 were having such jolly fun they reversed the words too: quefrency => frequency, saphe => phase, alanysis => analysis, liftering => filtering
The cepstrum is the "spectrum of a log spectrum," where taking the complex logarithm turns multiplicative spectral features into additive ones, laying the foundation of cepstral alanysis, and later, the physiologically tuned Mel-frequency cepstrum used in audio compression and speech recognition.
https://en.wikipedia.org/wiki/Mel_scale
>The mel scale (after the word melody)[1] is a perceptual scale of pitches judged by listeners to be equal in distance from one another. [...] Use of the mel scale is believed to weigh the data in a way appropriate to human perception.
As Tukey might say: once you start doing cepstral alanysis, there’s no turning back, except inversely.
Skeptics said he was just going through a backwards phase, but it turned out to work! ;)
https://news.ycombinator.com/item?id=24386845
DonHopkins on Sept 5, 2020 | parent | context | favorite | on: Mathematicians should stop naming things after eac...
I love how they named the inverse spectrum the cepstrum, which uses quefrency, saphe, alanysis, and liftering, instead of frequency, phase, analysis and filtering. It should not be confused with the earlier concept of the kepstrum, of course! ;)
https://en.wikipedia.org/wiki/Cepstrum
>References to the Bogert paper, in a bibliography, are often edited incorrectly. The terms "quefrency", "alanysis", "cepstrum" and "saphe" were invented by the authors by rearranging some letters in frequency, analysis, spectrum and phase. The new invented terms are defined by analogies to the older terms.
>Thus: The name cepstrum was derived by reversing the first four letters of "spectrum". Operations on cepstra are labelled quefrency analysis (aka quefrency alanysis[1]), liftering, or cepstral analysis. It may be pronounced in the two ways given, the second having the advantage of avoiding confusion with "kepstrum", which also exists (see below). [...]
>The kepstrum, which stands for "Kolmogorov-equation power-series time response", is similar to the cepstrum and has the same relation to it as expected value has to statistical average, i.e. cepstrum is the empirically measured quantity, while kepstrum is the theoretical quantity. It was in use before the cepstrum.[12][13]
https://news.ycombinator.com/item?id=43341806
DonHopkins 7 months ago | parent | context | favorite | on: What makes code hard to read: Visual patterns of c...
Speaking of filters and clear ergonomic abstractions, if you like programming languages with keyword pairs like if/fi, for/rof, while/elihw, goto/otog, you will LOVE the cabkwards covabulary of cepstral quefrency alanysis, invented in 1963 by B. P. Bogert, M. J. Healy, and J. W. Tukey:
cepstrum: inverse spectrum
lifter: inverse filter
saphe: inverse phase
quefrency alanysis: inverse frequency analysis
gisnal orpcessing: inverse signal processing
https://en.wikipedia.org/wiki/Cepstrum
https://news.ycombinator.com/item?id=44062022
DonHopkins 5 months ago | parent | context | favorite | on: The scientific “unit” we call the decibel
At least the Mel-frequency cepstrum is honest about being a perceptual scale anchored to human hearing, rather than posing as a universally-applicable physical unit.
https://en.wikipedia.org/wiki/Mel-frequency_cepstrum
>Mel-frequency cepstral coefficients (MFCCs) are coefficients that collectively make up an MFC. They are derived from a type of cepstral representation of the audio clip (a nonlinear "spectrum-of-a-spectrum"). The difference between the cepstrum and the mel-frequency cepstrum is that in the MFC, the frequency bands are equally spaced on the mel scale, which approximates the human auditory system's response more closely than the linearly-spaced frequency bands used in the normal spectrum. This frequency warping can allow for better representation of sound, for example, in audio compression that might potentially reduce the transmission bandwidth and the storage requirements of audio signals.
https://en.wikipedia.org/wiki/Psychoacoustics
>Psychoacoustics is the branch of psychophysics involving the scientific study of the perception of sound by the human auditory system. It is the branch of science studying the psychological responses associated with sound including noise, speech, and music. Psychoacoustics is an interdisciplinary field including psychology, acoustics, electronic engineering, physics, biology, physiology, and computer science.
Re: How the cochlea computes (2024)
#94The thesis about human speech occupying less crowded spectrum is well aligned with a book called "The Great Animal Orchestra" ( https://www.amazon.com/Great-Animal-Orchestra-Finding-Origin... ). That author details how the "dawn chorus" is composed of a vast number of species making noise, but who are able to pick out mating calls and other signals due to evolving their vocalizations into unique sonic niches. It's qu…
Probably worth mentioning that as evolutions that allow them to compete well in nature die out, ones that allow them to compete well in cities takes their place. Evolution is always a series of tradeoffs. Maybe we don't have sonic variation, but temporal instead.
Life uh, finds a way.
Re: How the cochlea computes (2024)
#95Many versions of this article could be written:
The computer does not do a Fourier transform (FFT computes the discrete Fourier transform)
Spectroscope dont do a Fourier transform (it's actually the short time FT)
The only thing that actually does Fourier transform is a mathematician, with a pen and some paper.
Re: How the cochlea computes (2024)
#96Earlier quoted context omitted.
> it also could just have a lot to do with the fact that, well, they have tiny articulators and tiny vocalizations! 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.
Well without the humorous size difference, this is basically what whales and elephants do for long distance communication.
Was playing around with a fundamental frequency calculator [0] to associate certain sizes to hertz, then using a tone-generator [1] to get a subjective idea of what it'd sound like.
Though of course, nature has plenty of other tricks, like how Koalas can go down to ~27hz. [2]
[0] https://acousticalengineer.com/fundamental-frequency-calcula...
Re: How the cochlea computes (2024)
#97Re: How the cochlea computes (2024)
#98Nice to see a video for the tip links and ion channels.
I spent a while reading up on that stuff because I was trying to figure what causes my tinnitus. My best guess is if the hairs over bend, that stuff can break and an ion channel get stuck open causing the cell to fire continually.
Another fun ear fact is they incorporate active amplification. You can hook an electrical signal to the loudspeaker type cell to make it vibrate around https://youtu.be/pij8a8aNpWQ
Re: How the cochlea computes (2024)
#99Earlier quoted context omitted.
Shave and a haircut is the only option in my knocking decision tree.
... What does that mean?
Re: How the cochlea computes (2024)
#100[deleted]