There are a number of authors and a number of contributors to this NG who claim that sampling of analogue signals is represented by multiplying the incoming waveform f(t) by a comb of Diracian Delta Functions of the form d(t - T) and who then go on to claim that each such sample gives rise to a contribution to the spectrum of the sampled signal of f(T).e^(-sT). As this claim, this apparently faulty meme, ought to be such a fundamental part of DSP, its foundation stone in fact, it should be possible to prove this assertion by appeal to Dirac's properties of his Delta Function, and to the Laplace transform. I think that such a proof should be a simple thing to be provided by that body of authors and contributors if the claim were to be true. In our training of the Laplacian method, we are presented with a whole range of such derivations, the spectra for d(t), u(t), t, sin(t), rect(t), sinc(t), etc etc etc. Why not a similar derivation for f(t).d(t - T)? It cannot be a difficult matter for those who make the claim that sampling is so represented! As that body of authors and contributors seem unable to provide such a proof and resort to side issues and rather silly and childish ad hominem attacks when challenged upon the matter the conclusion that I reach is that the claim is false, and that that body of authors and contributors hold a religious-like stance to the matter and respond with the emotional maladjustment which is the mark of all those who are the religious loonies of the world today. (11/9 and the resultant war brought on by the religionists Bush, Blair and Windsor being prime examples of catastrophes brought on by emotional maladjustment)

There are a number of authors and a number of contributors to this NG who claim that sampling of analogue signals is represented by multiplying the incoming waveform f(t) by a comb of Diracian Delta Functions of the form d(t - T) and who then go on to claim that each such sample gives rise to a contribution to the spectrum of the sampled signal of f(T).e^(-sT). As this claim, this apparently faulty meme, ought to be such a fundamental part of DSP, its foundation stone in fact, it should be possible to prove this assertion by appeal to Dirac's properties of his Delta Function, and to the Laplace transform. I think that such a proof should be a simple thing to be provided by that body of authors and contributors if the claim were to be true. In our training of the Laplacian method, we are presented with a whole range of such derivations, the spectra for d(t), u(t), t, sin(t), rect(t), sinc(t), etc etc etc. Why not a similar derivation for f(t).d(t - T)? It cannot be a...

It is clear that it is your intention to troll.

Derivation Of The Spectrum Due To f(t).d(t

Derivation Of The Spectrum Due To f(t).d(t - T)?????

Nov 28, 2004 285 Replies

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David C. Ullrich 21 years ago

There are no such functions. The so-called delta function is not a function.

Only seems that way to you.

No I didn't. Look it up - what I _stated_ that sounds something like that was something totally different.

Huh?

Interesting possibility. Let's check this out... Hmm, we see many people complaining about your trolling and nobody complaining about mine. So no, I don't think your conjecture holds water.

Guffaw.

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David C. Ullrich

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David Kastrup 21 years ago

In support of his conjecture, you are called "David" like I am and at least I am participating in a chorus of trolls in "Peer Gynt" next year.

While this is just a bit of coincidal evidence, it may become more compelling if I throw in a heartfelt

"Flæng ham! Flæng ham! Flæng ham! Flæng ham!"

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David C. Ullrich 21 years ago

heh-heh. Good point - so there are arguments on both sides.

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David C. Ullrich

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Bob Cain 21 years ago

If irony was sold by the ton...

Bob

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Airy R. Bean 21 years ago

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David Kastrup 21 years ago

The ton already was full, but thanks anyway.

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