# A Sound Mathematical Basis For Sampling - Lesson 1

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Good Morning, Boys and Girls, (and those of you with the mental and emotional age of Boys and Girls)

In this series of lectures I am going to deliver to you a sound mathematical basis for the sampling of analogue signals.

(In doing so, I may offend those of you who, in response to previous explanations offered by the so-called experts, have taken the religious loony's approach of resorting to illogical make-believe and defending that make-believe angrily against all-comers and that would be unfortunate. If, like all religious loonies, you have a closed mind, then I recommend that you attend another series of lectures because otherwise you will only get annoyed and start mouthing off personal remarks. I suggest that the class on Radio & TV Servicing will suit best those of you who are uppity technicians relying on "hands-on" experience and folklore together rather than the engineer's sound mathematical basis.)

I will deal with any questions at the end of the lecture series.

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There is a pre-requisite standard of mathematics that you will need. You must have completed a course of mathematics to the Brit "A" Level standard that existed 25 years ago, (and definitely not the Brit "A" Level standard of today which is more akin to an NVQ ("Not Very Qualified") than it is to an acadaemic achievement) and studied complex variable theory up to the point of its application to Fourier and Laplace. I will assume that you are au fait at this level, together with a good grounding in The Calculus.. This means, I suppose, that I expect you to be fully conversant with analogue signal processing at the undergraduate level.

If you are so conversant, then I will guarantee that you will _UNDERSTAND_ the sampling process rather than just repeating parrot fashion something which worried you but which you previously skipped over.

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So, to the first technical snippet, which starts to address the mantra of the religious loony and is entitled, "How not to explain a circuit".

Let us suppose that you are early in your "Oscillators and Amplifiers" course and you are seeking explanation of how a simple notionally-sine-wave oscillator works. That oscillator might be a phase-shifter with a low pass filter following, or it might be the slightly more complex compensated Wien Bridge circuit...

How not to explain, "The cosine signal may be analysed as consisting of two complex exponential signals, 0.5*e^(jwt) + 0.5e^(-jwt). These are generated separately and combined at the output of the oscillator to produce the cosine."

Such an explanation will produce howls of protest, and rightly so, because a request for a circuit explanation has provoked an explanation in terms of two _OTHER_ oscillators which do not even exist!

That's enough for today, see you tomorrow!