[kragen]

> 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]

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]

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]

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]

It's analogous to both, from different valid points of view.

[lonelappde]

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]

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.