On Sun, Mar 09, 2014 at 12:35:34AM +0200, Sampo Syreeni wrote: > There are four basic forms of the theory used in signal processing, > which are all connected but also subtly different. The Fourier > transform is continuous time and continuous frequency. The Fourier > series is periodic time and discrete frequency. The discrete time > Fourier transform is discrete time and periodic frequency. And > finally the discrete Fourier transform is both discrete and periodic > in both frequency and in time.
There are just two, the FT and the DFT. The only difference between the last three forms you mention is only a matter of interpretation. Usually a discrete spectrum is interpreted as the exact spectrum of a periodic waveform. But it's equally valid to say its the sampled spectrum of a finite time signal. A discrete representation in the time domain (i.e. samples) is usually interpreted as a finite-bandwidth signal (which is the dual of the second interpretation above), but it's equally valid to say it's the exact representation of a signal that is periodic in the frequency domain (the dual of the first interpretation above). 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 Sursound@music.vt.edu https://mail.music.vt.edu/mailman/listinfo/sursound
