22 ms·

Cat meow sounds visualized with auto-correlation function

38 points by ssgh 5y ago

errantspark 5y ago
Is "dropping the phase" the same thing as computing the spectral power distribution? P.S. A4 = 432Hz is a stupid fad that can't die soon enough.
- dylan604 5y ago
  To quote the dude, "that's like your opinion, man." For others less familiar with this poster's preference and their angst: https://producerhive.com/editorial/432hz-vs-440hz/ https://producerhive.com/editorial/432hz-vs-440hz/
- jarenmf 5y ago
  Seems so, except that in this case it is basically just the modulus whereas the PSD is the modulus squared |A|^2
  - errantspark 5y ago
    Ahh yeah, magnitude vs. power, my mistake on the terms.
- gbh444g 5y ago
  432 vs 440 Hz in music is the equivalent of the C++ vs Java battle. Vivaldi was a proponent of 432 Hz, so it's only when he died, newthinkers had recalibrated pianos to 440 Hz. I believe the newthinkers are simply lacking taste, and rounding 432 to 440 is same as chopping off a chunk of Parthenon to "fix" its proportions from the golden phi ratio to 3/2.
  - errantspark 5y ago
    No, it's not. Java and C++, hell even Java and C# are much more relevantly dissimilar than setting A at 440 vs 432. I'd love to see a citation on Vivaldi's love for 432, he wasn't even playing in 12-TET was he? He'd probably be playing in meantone during that era right? I figure he'd be way more mad about using the wrong intonation to play his music than a difference absolute pitch reference. > rounding 432 to 440 Rounding from what to what? Why does the number cycles relative to seconds being any particular number matter?
    - gbh444g 5y ago
      Well, I don't know. My personal reason is that 432 has at least some connection to reality, e.g. half day = 43,200 sec, or speed of light = 432 x 432 miles/sec, or Sun's radius = 432,000 miles. This means that if we take distance that light covers in 1/432 sec, then Sun's radius is exactly 1000 such distances, which is pretty cool. On the other hand, 440 Hz seems just a random number to me picked by someone with little imagination.
nixpulvis 5y ago
Cool idea progressing time outwards radially, for a moment I thought I was looking at the cat's eye through a strange filter!
gbh444g 5y ago
Hi HN! I used the meow sounds from https://soundspunos.com/animals/10-cat-meow-sounds.html https://soundspunos.com/animals/10-cat-meow-sounds.html. I expected to see very little variability in the meows, maybe just 4-5 different types for basic emotions. To my surprise, each “cat meow” has astonishingly colorful, complex and unique structure, unlike human vowels that follow a more or less predictable pattern: https://soundshader.github.io/vowels https://soundshader.github.io/vowels. The algorithm behind these images is fairly simple. It computes FFT to decompose the sound into a set of A·cos(2πwt+φ) waves and drops the phase φ to align all cos waves together. This is known as the auto-correlation function (ACF). Before merging them back, it colorizes each wave using its frequency w: the A notes (432·2ⁿ Hz) become red, C notes - green, E notes - blue, and so on. Finally, it merges the colored and aligned cos waves back, using the amplitude A for color opacity, and renders them in polar coordinates, where the radial coordinate is time.
- vanusa 5y ago
  I would agree that the images are rather intriguing, but ... what does all this visual structure actually mean? I'm guessing some kind of overtone structure in these sounds (perhaps decipherable to cats, but not to us)? I await your insight.
  - nixpulvis 5y ago
    I know from personal experience, cat's use a lot of inflection in their voices. I'm not at all surprised by the images (though I don't know exactly what they mean). This inflection directly effects the image, because it modulates the pitch of the meow. Another factor, completely unrepresented in these images is the lower frequency components connected by seconds of silence. Most cats are pretty quiet, but sometimes they get the oral equivalent of the zoomies. I would love to see more examples across species and variants of felines, under controlled conditions. Could you figure out an appropriate color map? Not to start a dog vs cat war, but as someone who loves both, I think I can safely say that cats put much more information in their voices than dogs, for example.
    - 5y ago
RosanaAnaDana 5y ago
Things like this are why I go on the internet.
hereforphone 5y ago
> It computes FFT to decompose the sound into a set of A·cos(2πwt+φ) waves and drops the phase φ to align all cos waves together. This is known as the auto-correlation function (ACF). How is simply dropping the phase transforming FFT into ACF (according to various definitions of ACF as shown here: https://en.wikipedia.org/wiki/Autocorrelation https://en.wikipedia.org/wiki/Autocorrelation)?
- jarenmf 5y ago
  I might be mistaken but since the auto-correlation function is the inverse FFT of the power spectral density and power spectral density doesn't contain information about the phase. Thus, it's like dropping the phase and taking IFFT(|A|^2)
  - hereforphone 5y ago
    They're inverse operations but as far as I understand that's not the only thing going on with the ACF. Taking the phase out is just taking the real part of the FFT is it not? Regardless where's the correlation?
- gbh444g 5y ago
  Wikipedia is great at obfuscating simple ideas in complex math. The "Efficient computation" explains the idea well, but it could be made even simpler. The amplitude squaring step drops the phase there.
  - hereforphone 5y ago
    The phase is dropped but isn't there more going on? Comparing the signal to itself at various lags? I don't see how just dropping the phase accomplishes that.
    - gbh444g 5y ago
      Not really. ACF is defined as a convolution of signal X with itself: XX. But FFT turns a convolution into a dot product: FFT[XX] = FFT[X]·FFT[X], or just |FFT[X]|². But what is this really? If X is a sum of A·cos(2πwt+φ) waves, then FFT[X] is a set of A·exp(iφ) complex numbers. What does |FFT[X]|² do? It turns those complex numbers into A². Inversing this FFT gives a sum of A²·cos(2πwt) waves, so in effect ACF has dropped the phases and squared amplitudes. This is also why ACF have this bright vertical line - this is cos(x) functions piling up together.
beebeepka 5y ago
Not sure how these images are being generated but in my experience there is a wide variety of purr and meow. Can't say unique because I have no way of knowing. Cats are magical to me but in reality I can be friends with all sorts of animals, even people!
rawling 5y ago
Well, I guess this one is never going to be more relevant: https://xkcd.com/26 https://xkcd.com/26
- ssgh 5y ago
  The xkcd is half-right. Cats are ACFs, not FFTs, because they are even functions in polar coordinates, I mean the left half of the cat mirrors the right half, and the two halves merge nicely, without discontinuities. I probably don't want to know what cats look like with the phase components restored.

38 points by ssgh 5y ago

Is "dropping the phase" the same thing as computing the spectral power distribution? P.S. A4 = 432Hz is a stupid fad that can't die soon enough.

dylan604 5y ago
To quote the dude, "that's like your opinion, man." For others less familiar with this poster's preference and their angst: https://producerhive.com/editorial/432hz-vs-440hz/ https://producerhive.com/editorial/432hz-vs-440hz/
jarenmf 5y ago
Seems so, except that in this case it is basically just the modulus whereas the PSD is the modulus squared |A|^2
- errantspark 5y ago
  Ahh yeah, magnitude vs. power, my mistake on the terms.
gbh444g 5y ago
432 vs 440 Hz in music is the equivalent of the C++ vs Java battle. Vivaldi was a proponent of 432 Hz, so it's only when he died, newthinkers had recalibrated pianos to 440 Hz. I believe the newthinkers are simply lacking taste, and rounding 432 to 440 is same as chopping off a chunk of Parthenon to "fix" its proportions from the golden phi ratio to 3/2.
- errantspark 5y ago
  No, it's not. Java and C++, hell even Java and C# are much more relevantly dissimilar than setting A at 440 vs 432. I'd love to see a citation on Vivaldi's love for 432, he wasn't even playing in 12-TET was he? He'd probably be playing in meantone during that era right? I figure he'd be way more mad about using the wrong intonation to play his music than a difference absolute pitch reference. > rounding 432 to 440 Rounding from what to what? Why does the number cycles relative to seconds being any particular number matter?
  - gbh444g 5y ago
    Well, I don't know. My personal reason is that 432 has at least some connection to reality, e.g. half day = 43,200 sec, or speed of light = 432 x 432 miles/sec, or Sun's radius = 432,000 miles. This means that if we take distance that light covers in 1/432 sec, then Sun's radius is exactly 1000 such distances, which is pretty cool. On the other hand, 440 Hz seems just a random number to me picked by someone with little imagination.

nixpulvis 5y ago

Cool idea progressing time outwards radially, for a moment I thought I was looking at the cat's eye through a strange filter!

gbh444g 5y ago

Hi HN! I used the meow sounds from https://soundspunos.com/animals/10-cat-meow-sounds.html https://soundspunos.com/animals/10-cat-meow-sounds.html. I expected to see very little variability in the meows, maybe just 4-5 different types for basic emotions. To my surprise, each “cat meow” has astonishingly colorful, complex and unique structure, unlike human vowels that follow a more or less predictable pattern: https://soundshader.github.io/vowels https://soundshader.github.io/vowels. The algorithm behind these images is fairly simple. It computes FFT to decompose the sound into a set of A·cos(2πwt+φ) waves and drops the phase φ to align all cos waves together. This is known as the auto-correlation function (ACF). Before merging them back, it colorizes each wave using its frequency w: the A notes (432·2ⁿ Hz) become red, C notes - green, E notes - blue, and so on. Finally, it merges the colored and aligned cos waves back, using the amplitude A for color opacity, and renders them in polar coordinates, where the radial coordinate is time.

vanusa 5y ago
I would agree that the images are rather intriguing, but ... what does all this visual structure actually mean? I'm guessing some kind of overtone structure in these sounds (perhaps decipherable to cats, but not to us)? I await your insight.
- nixpulvis 5y ago
  I know from personal experience, cat's use a lot of inflection in their voices. I'm not at all surprised by the images (though I don't know exactly what they mean). This inflection directly effects the image, because it modulates the pitch of the meow. Another factor, completely unrepresented in these images is the lower frequency components connected by seconds of silence. Most cats are pretty quiet, but sometimes they get the oral equivalent of the zoomies. I would love to see more examples across species and variants of felines, under controlled conditions. Could you figure out an appropriate color map? Not to start a dog vs cat war, but as someone who loves both, I think I can safely say that cats put much more information in their voices than dogs, for example.
  - 5y ago

RosanaAnaDana 5y ago

Things like this are why I go on the internet.

hereforphone 5y ago

> It computes FFT to decompose the sound into a set of A·cos(2πwt+φ) waves and drops the phase φ to align all cos waves together. This is known as the auto-correlation function (ACF). How is simply dropping the phase transforming FFT into ACF (according to various definitions of ACF as shown here: https://en.wikipedia.org/wiki/Autocorrelation https://en.wikipedia.org/wiki/Autocorrelation)?

jarenmf 5y ago
I might be mistaken but since the auto-correlation function is the inverse FFT of the power spectral density and power spectral density doesn't contain information about the phase. Thus, it's like dropping the phase and taking IFFT(|A|^2)
- hereforphone 5y ago
  They're inverse operations but as far as I understand that's not the only thing going on with the ACF. Taking the phase out is just taking the real part of the FFT is it not? Regardless where's the correlation?
gbh444g 5y ago
Wikipedia is great at obfuscating simple ideas in complex math. The "Efficient computation" explains the idea well, but it could be made even simpler. The amplitude squaring step drops the phase there.
- hereforphone 5y ago
  The phase is dropped but isn't there more going on? Comparing the signal to itself at various lags? I don't see how just dropping the phase accomplishes that.
  - gbh444g 5y ago
    Not really. ACF is defined as a convolution of signal X with itself: XX. But FFT turns a convolution into a dot product: FFT[XX] = FFT[X]·FFT[X], or just |FFT[X]|². But what is this really? If X is a sum of A·cos(2πwt+φ) waves, then FFT[X] is a set of A·exp(iφ) complex numbers. What does |FFT[X]|² do? It turns those complex numbers into A². Inversing this FFT gives a sum of A²·cos(2πwt) waves, so in effect ACF has dropped the phases and squared amplitudes. This is also why ACF have this bright vertical line - this is cos(x) functions piling up together.

beebeepka 5y ago

Not sure how these images are being generated but in my experience there is a wide variety of purr and meow. Can't say unique because I have no way of knowing. Cats are magical to me but in reality I can be friends with all sorts of animals, even people!

rawling 5y ago

Well, I guess this one is never going to be more relevant: https://xkcd.com/26 https://xkcd.com/26

ssgh 5y ago
The xkcd is half-right. Cats are ACFs, not FFTs, because they are even functions in polar coordinates, I mean the left half of the cat mirrors the right half, and the two halves merge nicely, without discontinuities. I probably don't want to know what cats look like with the phase components restored.