I was going to do a proper blog post to interrupt my silence; unfortunately I’m having difficulty in getting the TeX to work properly. In particular, for some reason the formulas don’t appear in the right place.

Anyway, this is material that I learned from a course of Sinan Güntürk; once they’re ready, I’ll post the notes I take.

What I’m posting here now states that signals whose frequencies are bounded can be recovered entirely from sampling at a discrete set of points provided the sampling mesh is sufficiently small. This fact was popularized by Shannon in his fundamental paper on information theory.

Here is the file.

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January 26, 2010 at 6:41 pm

Regarding the sampling theorem the main result I learned back in the 1970s as an engineering undergraduate was as follows:

A function whose spectrum is limited to the frequence bandwidth is fully defined by a sequence of values , where is the repetition period and is an arbitrary instant.

January 28, 2010 at 7:17 pm

Sorry about that! Apparently the spam filter flagged your comment while I was not paying attention.

January 28, 2010 at 8:11 pm

No problem. I have to learn some mathematical concepts and notation to compare your paper with the statement I quoted from a Portuguese telecommunications book written in 1968.

Thanks!