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I was loose w/ words, but I maintain there is inherent compression aspect to Fourier transform, because for a large class of signals, most of the energy is cont
by cdavid 6y ago
I was loose w/ words, but I maintain there is inherent compression aspect to Fourier transform, because for a large class of signals, most of the energy is contained in the first few coefficients. See also the similarity between fourier transforms and KL transform for random variables, itself related to PCA.
Ofc, it depends on what you mean exactly by compression. At least for audio, it relates well to keeping the main signal quality because in a sense, the earing system does a frequency decomposition (see e.g. https://www.ncbi.nlm.nih.gov/books/NBK10946/figure/A896/?report=objectonly https://www.ncbi.nlm.nih.gov/books/NBK10946/figure/A896/?rep...), and the higher the frequency, the less sensitive to it we tend to be.
- Jasper_ 6y agoRight. The DCT, in theory, is completely lossless. But the reason that the "other space" is helpful for us for compression is because our eyes and ears are more interested in comparing relatively than absolutely. So you don't need the exact high-frequency content, just the relatively correct high-frequency content. As discussed, "high-frequency" just means stuff that's moving very fast. In sound, that's compared to pitch. In a JPEG image, that means a given pixel's brightness. This is what the DCT is exploiting -- that we can adjust the high-frequency terms and it will still look OK to our eyes. https://magcius.github.io/dctx/ https://magcius.github.io/dctx/