6 ms·

Its comparing 1 dimensional space to 2 demential space. So, any comparison is gong to be a little hand wavy. But temporally, I believe the comparison is apt.

kragen 7y ago
> Its comparing 1 dimensional space to 2 demential space Although I love the coinage "2 demential space", I think you mean "comparing one-dimensional space [audio] to three-dimensional space [video]". A two-dimensional signal might be a still image or a temporal sequence of samples from a one-dimensional array of sensors, such as those in a single slice of a CT machine or a linear MIMO antenna array. A video signal is three-dimensional, not two-dimensional, and probably not "2 demential" either.
- slimscsi 7y ago
  Including pixel intensity, you are correct. Infact it has thee planes, so you could even call it 9 demential If you break it down that way.
  - kragen 7y ago
    No, wavelength is just one more dimension along which intensity may vary (in addition to X, and Y, and time), not five or six more dimensions, so a multi-band image is only three-dimensional, regardless of whether there are three wavelength bands (like RGB or YCbCr), four (like RGBA), 8 (like Landsat), or 210 (like HYDICE, AVIRIS, and other imaging spectrometers).
    - slimscsi 7y ago
      My point is, I am comparing temporal dimension to temporal dimension regardless of how many special dimensions there are. And I don’t understand the argument that an audio sample is more analogous to a pixel that it is a frame on a time line.
      - kragen 7y ago
        It's analogous to both, from different valid points of view.
        lonelappde 7y ago
        In particular, in data processing, all dimensionality is equivalent, since and infinite set S the same cardinality as S^n for any whole number n, and any finite set is smaller than the 1-dimensional set of naturals.
        kragen 7y ago
        Yeah, at least if Hilbert spaces can fuck off, which is why we can approximate signal processing on digital computers at all. And, because of space-filling curves, in some sense ℝⁿ is equivalent to ℝ. But, to understand signal processing, a much more useful point of view is that ℝⁿ is significantly different for different values of n, but not completely unrelated; and ℤⁿ is a useful approximation of ℝⁿ, as is (ℤ/mℤ)ⁿ.

kragen 7y ago

> Its comparing 1 dimensional space to 2 demential space Although I love the coinage "2 demential space", I think you mean "comparing one-dimensional space [audio] to three-dimensional space [video]". A two-dimensional signal might be a still image or a temporal sequence of samples from a one-dimensional array of sensors, such as those in a single slice of a CT machine or a linear MIMO antenna array. A video signal is three-dimensional, not two-dimensional, and probably not "2 demential" either.

slimscsi 7y ago
Including pixel intensity, you are correct. Infact it has thee planes, so you could even call it 9 demential If you break it down that way.
- kragen 7y ago
  No, wavelength is just one more dimension along which intensity may vary (in addition to X, and Y, and time), not five or six more dimensions, so a multi-band image is only three-dimensional, regardless of whether there are three wavelength bands (like RGB or YCbCr), four (like RGBA), 8 (like Landsat), or 210 (like HYDICE, AVIRIS, and other imaging spectrometers).
  - slimscsi 7y ago
    My point is, I am comparing temporal dimension to temporal dimension regardless of how many special dimensions there are. And I don’t understand the argument that an audio sample is more analogous to a pixel that it is a frame on a time line.
    - kragen 7y ago
      It's analogous to both, from different valid points of view.
      - lonelappde 7y ago
        In particular, in data processing, all dimensionality is equivalent, since and infinite set S the same cardinality as S^n for any whole number n, and any finite set is smaller than the 1-dimensional set of naturals.
        kragen 7y ago
        Yeah, at least if Hilbert spaces can fuck off, which is why we can approximate signal processing on digital computers at all. And, because of space-filling curves, in some sense ℝⁿ is equivalent to ℝ. But, to understand signal processing, a much more useful point of view is that ℝⁿ is significantly different for different values of n, but not completely unrelated; and ℤⁿ is a useful approximation of ℝⁿ, as is (ℤ/mℤ)ⁿ.