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When signal processing experts say something is analogue, what do they mean?

If I understand correctly from prior research, they mean to an analogue system, i.e. a system with by-definition uncountable number of modes/states.

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  • $\begingroup$ @MarcusMüller I doubt it, I am not asking what is an analogue signal but what is analogue at all. Digital is easy (involves digits), but analogue? $\endgroup$
    – beltazzar
    Oct 9, 2022 at 16:32
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    $\begingroup$ Digital = involves digits: no, it's not that easy. You really want to understand that question and the answer. $\endgroup$ Oct 9, 2022 at 16:35
  • $\begingroup$ @MarcusMüller Digital in a general or etymological meaning does mean, as you well know, something that involves digits (countable, finite, if you will) I was referring only to that. I am aware that the definitions used by signal processing experts are much more complex and are mathematical. $\endgroup$
    – beltazzar
    Oct 9, 2022 at 19:52

2 Answers 2

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When signal processing experts say something is analogue, what do they mean?

In almost all cases they mean that something is "continuous" and not "discrete". Specifically it means "time continuous", i.e. a signal is defined at all points in time. "Time discrete" in contrast means that the signal only defined at specific points in time and therefore can be represented as a "list of numbers".

It often also means "amplitude continuous" in contrast to "amplitude discrete" but that distinction is less important. Most signals are either continuous or discrete in both domains.

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  • $\begingroup$ About your last sentence, are you saying that most signals are both continuous and discrete? $\endgroup$
    – beltazzar
    Oct 9, 2022 at 18:16
  • $\begingroup$ What I'm saying is that in practice most time discrete signals are also amplitude discrete and most time continuous signals are also amplitude continuous. They can be converted into each other by using DAC or ADC (Analog to Digital Converter ) $\endgroup$
    – Hilmar
    Oct 10, 2022 at 7:15
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I'm not sure what you mean by "unaccountably infinite" modes/states". In computer science, if you have one variable that can take on multiple states such as "green", "red", "fuchsia", "potato", "rhizome" then that's a state variable with five states. In dynamic systems, that's a state, that can take on five values. I will be using the dynamic systems definition of "state" in my answer.

Usually if the word "analog" pops up it refers to a system whose states take on continuous values and whose time domain is continuous. This can either be a system with a finite number of states/modes (albeit continuous ones) that can be represented as an ordinary differential equation, i.e. $$\ddot x = -a \dot x - b x, \tag 1$$ or it could refer to a system with an infinite number of modes that must be represented by a partial differential equation, i.e. $$\frac{\partial \phi(\mathbf x, t)}{\partial t} = D \nabla^2 \phi(\mathbf x, t). \tag 2$$

This comes from the definition of "analog electronics", which (as far as I know, I'm not an etymologist) comes from simulating physical phenomena using analog computers, which build an electrical or mechanical analog of some system you want to simulate, i.e. they embody differential equations that represent your original system.

The converse of "analog" in this context is "digital". Which is ironic, because if you're using a digital computer to simulate a system, you first build a program that contains a digital analog of the system you're trying to study.

In practical terms, a digital system is one whose states take on a finite (if large) number of discrete values. In nearly all practical cases, a digital system is also one that operates in discrete time, although there are older systems out there that have -- essentially -- digital sub-systems that take on discrete numbers of states but do so in continuous time.

Almost always in signal processing, the system that you build has a finite number of states. "Digital signal processing" pretty much exclusively refers to systems that have a finite number of states that operate in sampled time. During the analysis phase of design, these states are usually treated as taking on continuous values -- but aren't called "analog". Actual implementation always* happens in digital computing hardware, at which point the realization is, in fact, digital.

* To my knowledge. There may be some very old, or very fast, systems that don't.

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