On Sat, Jun 29, 2013 at 06:13:19PM -0700, Robert Greene wrote: > I do not understand the last bit of this message below at all. > There is no such thing as a signal that is limited > in bandwidth and in time--not if limited > means actually 0 outside a finite interval > in both cases. This is a basic result of Fourier > analysis. > This kind of signal does not exist, not mathematically > and of course not physically either.
True of course. But in practice you can get as close as you want, and we do this all the time and just ensure that the remaining errors are small enough to be of no consequence. None of the digital audio equipment we use would be able to work if it had 'perfect' antialias filters for example, it would take infinite time to convert the first sample. The thing I wanted to point out was the duality between: A. If a signal is limited in the F domain it can be represented by samples in the T domain (Nyquist), and B. If a signal is limited in the T domain it can be represented by samples in the F domain (i.e. by a discrete spectrum). In both cases there is the implicit assumption that the 'other' domain is infinite. For (A) we accept some aliasing in the F domain but outside the audible band. For (B) we have to accept some leakage in the T domain, which would show up as small errors near the start and end of the time interval. Ciao, -- FA A world of exhaustive, reliable metadata would be an utopia. It's also a pipe-dream, founded on self-delusion, nerd hubris and hysterically inflated market opportunities. (Cory Doctorow) _______________________________________________ Sursound mailing list [email protected] https://mail.music.vt.edu/mailman/listinfo/sursound
