Discrete and continuous signal processing

[flemmyd]

First, I'm not an engineer, so I don't know this topic very well.

Anyway, we were covering Fourier Transforms in one of my analytical methods class (chem major; NMR was the topic) and the phrase "discrete signal processing" came up.

In our particular case, we collect individual points on the freq domain, do a FT and that gives us our data.

my question was: how does this related to continuous signal processing? it seems like the only way to get a continuous sample is to take an infinite number of data points- which is impossible, right?

 

[marcusl]

It is a fundamental theorem of signal processing that the continuous signal can be reconstructed exactly from samples that are uniformly spaced by time T_s, so long as the sampling rate F_s=1/T_s is equal to or greater than EDIT: twice the highest frequency component in the signal. This is known as Shannon's sampling theorem, although it was discovered independently by others (Kotelnikov in Russia, the English mathematician Whittaker, etc.).

You say you sample in frequency, which doesn't make sense. In NMR it is usually time domain data that are collected, sampled and transformed to the frequency domain. However a version of the theorem works in reverse anyway since the FT is symmetric between the two domains.

 

[Bob S]

my question was: how does this related to continuous signal processing? it seems like the only way to get a continuous sample is to take an infinite number of data points- which is impossible, right?

A simple example of continuous signal processing is to take a discrete 1-second sample, and add it to 90% of the total sample (multiply the old sample by 0.9) for the previous second. Thus the total sample is quasi-continuous, and evolves as the sample signal changes. Usually, the blending of new and old signals is much faster, and the discreteness cannot be seen on a network analyzer.

Bob S