Should this page link to isochronous signal for the uniform sampling rate case? And can we say anything else about the nonuniform sampling rate case?
MusicScience 04:08, 12 June 2007 (UTC)
- A link wouldn't hurt, though there's not much there. Dicklyon 14:56, 12 June 2007 (UTC)
Discrete signal and discrete time are largely covering the same subject. I have no preference on what the combined article should be called, but the latter article is unreferenced and a large part of it consists of an example we could probably just drop. SpinningSpark 15:48, 8 June 2013 (UTC)
- I agree. Maybe call the new article Discrete-time signal. Radiodef (talk) 21:29, 10 August 2013 (UTC)
- I also support this merge. -- Mesoderm (talk) 21:35, 10 August 2013 (UTC)
That section says:
Uniformly sampled discrete-time signals can be expressed as the time-domain multiplication between a pulse train and a continuous time signal. This time-domain multiplication is equivalent to a convolution in the frequency domain. Practically, this means that a signal must be bandlimited to less than half the sampling frequency, i.e. Fs/2 - ε, in order to prevent aliasing.
Some important omissions are:
- The multiplicative model of sampling is the result of performing an inverse Fourier transform on a discrete-time Fourier transform. Mathematically dubious, but turns out to be useful. Right for the wrong reasons.
- Multiplication is a non-linear operation, which is the only kind of operation that can create frequency components (in this case "aliases") that aren't in the original signal.
Then it asserts:
Likewise, all non-linear operations performed on discrete-time signals must be bandlimited to Fs/2 - ε. Wagner's book Analytical Transients proves why equality is not permissible.
Help... I'm hard-pressed to think of any non-linear operation that is bandlimited.
No need to search the archives for a 55-year-old proof. It's a simple argument, found at Shannon_sampling_theorem#Critical_frequency.
- Wagner 1959