On Fri, 1 Aug 2014, Vadim Zavalishin wrote:
My quick guess is that bandlimited does imply analytic in the complex analysis sense.
1st off, I am fairly sure it is true that a BL signal cannot be zero over an interval, so two non-zero BL signals cannot differ by zero over an interval, so a function with cetain values over any interval is unique, so the rest of this may be cruft...
However, an audio signal is most often a real valued function of a real value or a complex valued function of a real value whos imaginary part happens to be zero (often almost interchangably to little ill effect.)
So to get an analytic complex function you'd have to extend the function. A non-zero analytic can't have a zero imaginary part, so we'd need a ``new'' imaginary part and to extent the real and imaginary parts to a neighborhood of the real line.
Off the cuff I think you might use the real values of f on the real axis as boundary conditions for the Cauchy-Reimann equations in a neighborhood of the real axis to solve for a non-zero imaginary part for f(z) which would then be analytic. This is /if/ BL is enough to show such a solution exists tehn you're done (which I do not claim is false. I just can't see a way to get there.)
Ron -- 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
