# A Sound Mathematical Basis For Sampling - Lesson 2

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Good Morning, Boys and Girls, (and those of you with the mental and emotional age of Boys and Girls; such age having been already demonstrated in your responses to Lesson 1. Perhaps there are those of you who, rather than coming up to University from high school, would have fared better by going back down to elementary school where you would find your equals in the playground?)

In today's lecture, I want to aim right at the heart of the subject matter - that of the sampling of analogue signals.

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I have two things that I need to point out. Firstly, to highlight that sampling circuits are not LTI, (Linear, Time Invariant) and therefore are not analysable by our tools from Laplace.

Certainly, we can describe the output signal that comes from our sampling circuits using Laplace, but we can neither describe, nor decompose, their operation using Laplace.

The sampling circuit is, in fact, a SIGNAL GENERATOR that is certainly controlled by the incoming analogue waveform but it is definitely NOT an LTI filter!

(A moment's thought will show the truth of this - if a sine-wave were to be presented to our sampling circuit, the output of the circuit would just not be represented by the convolution of that sine-wave with the output of the sampler)

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Secondly, I need to point out that the first-order hold presented as an attribute of the output of a DSP by many authors, is, in fact, an attribute of the input sampling. Samples are taken, and remain static until further samples are taken.

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.....I'm very sorry, children, I've been called away.

I'll continue with this tomorrow!