>It's my understanding that the fourier "theory" says any signal can be created >by summing various frequencies at various phases and amplitudes.
OK, now recall that the Fourier series describes a subset of “any signal” with a subset of “various frequencies”. It’s more like one cycle of any waveform can be created by summing sine waves of multiples of that cycle at various phases and amplitudes (a little awkward, but trying to modify your words). Fourier figured that out by observing the way heat traveled around an iron ring (hence the focus on cycles)–he wasn’t really into the recording scene back then ;-) (It’s true that Fourier techniques can be used to create more arbitrary signals, but that somewhat in the manner that movies are made from many still pictures.) So, it seems that you’re trying to match the theory of a very specific, limited portion of a signal, with one that doesn’t have those limitations. On Mar 26, 2014, at 9:46 PM, Doug Houghton <[email protected]> wrote: > > "There is the frequency-sensitive requirement that you can’t properly sample > a signal that has frequencies higher than half the sample rate. For music, > that’s not a problem, since our ears have a significant band limitation > anyway." > > This is intuitive. I think perhaps what I'm asking has more to do directly > with the fourier series than sample theory. > > It's my understanding that the fourier "theory" says any signal can be > created by summing various frequencies at various phases and amplitudes. So > this would answer my question then that it's not really a stipulation of the > function persay, since any signal at all can be described this way. > -- -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
