# Talk:Discrete-time signal

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)

## Suggested merge

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)
And I see Discrete-time signal already redirects to Discrete signal. Radiodef (talk) 21:30, 10 August 2013 (UTC)
I also support this merge. -- Mesoderm (talk) 21:35, 10 August 2013 (UTC)
Done. This has been open since June with no objections which I think is long enough. The original version of Discrete time can still be viewed in the history if anyone wants to look to see if anything else can be salvaged. SpinningSpark 09:23, 11 August 2013 (UTC)

## Time signals

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.[1]

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.

--Bob K (talk) 19:41, 4 December 2013 (UTC)

1. ^ Wagner 1959