1

Is digital necessarily discrete in both amplitude and time?

Or rather it is necessarily discrete only in time (but not necessarily in amplitude)?

yaraklis
  • 1
  • 1
  • 6
  • 1
    Every definition of digital signals is that it's both. If you find a different one, clearly say that you mean that. But Uroc327's answer is spot on: Usually it means discrete in both and you'd do good in adhering to that canonical definition. – Marcus Müller Mar 09 '22 at 14:51
  • 3
    Does this answer your question? What is the difference between continuous, discrete, analog and digital signal? – Marcus Müller Mar 09 '22 at 14:52
  • @MarcusMüller no, because I don't seek comparison with any other term than these mentioned in my post. Thank you. – yaraklis Mar 09 '22 at 15:32
  • 1
    I object. The accepted answer explicitly defines digital as time- AND value-discrete. So, yes, it does answer your question. – Marcus Müller Mar 09 '22 at 15:33
  • Sorry, my mistake in not saying "maybe" because I didn't read the linked post. Even if it is, the Q-A session is different due to a different question here, not involving the aforementioned terms. I avoid connecting posts with different questions by principle. – yaraklis Mar 09 '22 at 15:39
  • 1
    I avoid asking questions that others have answered already, then not reading the answers, then saying the answer don't answer my question ;) – Marcus Müller Mar 09 '22 at 15:48
  • @MarcusMüller in this website, no one answered my question (in the direct, simple sense of the word answering) besides Uroc327. The linked answer may include data which might have prevented me from asking my question but it's not an answer to my question. So I take back the maybe and bring back the "no". – yaraklis Mar 09 '22 at 16:17
  • "Maybe" can be an answer based on how one defines the term "answer" but clearly from what I wrote, it's not an answer if one distinguishes "something which prevents a question" from "filling of missing information" (I guess that's a nice way to put it). – yaraklis Mar 09 '22 at 16:22
  • 1
    The answer I linked to answers your question: it literally has "digital" in bold and above that what it means, "discrete t, discrete y(t)". I'm not blaming you for not finding it at all! It's just that your question is in fact answered by the answer. Though I must admit it was easy to find for me, I searched for definition of digital and read the first post that seemed to refer to a definition. – Marcus Müller Mar 09 '22 at 16:23
  • It doesn't answer my question because the question there is not Is digital necessarily discrete in both amplitude and time? and not something almost identical in my opinion, nonetheless not as focal. I don't care how easy it was to find for anyone. – yaraklis Mar 09 '22 at 16:24

3 Answers3

4

It's a matter of definition. Usually one defines digital to be discrete in both, discrete time to be (possibly) amplitude continuous and quantized to be (possibly) time continuous.

Uroc327
  • 231
  • 1
  • 5
2

Digital by definition means signals expressed using “digits” and those digits are typically “0” and “1”. This means a fixed point representation and need not be discrete-time to be digital (but most commonly is).

Therefore the one test is, is it expressed using “fixed point” representations; are the amplitude values quantized? If it is, it is digital. You can then go on to define if it is discrete time or continuous time.

Using that description, a discrete time system need not be “digital” if we haven’t quantized the amplitudes for each sample. (Such as a continuous time sample/hold).

As @MarcusMueller points out here, in Discrete Time Systems by Oppenheim & Schaefer, the authors define "digital systems" as being both discrete in time and discrete in frequency. In my own use, I would specifically distinguish the two interfaces of a D/A converter as being discrete in time and discrete in magnitude on the digital side, and being discrete in magnitude and continuous in time on the analog side (if we consider prior to reconstruction filtering the typical stair-case output of a DAC). With these thoughts in mind I would argue the typical convention for "Digital" with respect to signal processing is that it be both Discrete in Time and Discrete in Magnitude, and as @AlexTP defines, countably finite in magnitude (able to be described from a finite number of digits).

Dan Boschen
  • 50,942
  • 2
  • 57
  • 135
  • 1
    @MarcusMueller (Continuing here)...I am actually content with O&S definition as being complete: Digital is simply discrete in time and discrete in magnitude. I don't see the reason to condition it to also be a finite number of magnitudes (and similarly for finite time). Yes that is a condition to be physically realizable, but we often use descriptions from infinite sets- I don't think that is a reasonable requirement to exclude a fictitious infinite digital system, no different than our use of infinite spans for frequency and time. – Dan Boschen Mar 19 '22 at 15:07
  • 1
    The usage in "Oppenheim & Schaefer" is less a definition than a statement of what digital signals are discussed. It doesn't imply that continuous-time digital signals don't exist, just that you won't learn about them in that book (where the title immediately tells you that the scope is discrete time). – Ben Voigt Jan 11 '23 at 19:57
  • @BenVoigt Yes that’s a great comment. I agree with you—- as far as what establishes a definition I am not sure, perhaps we can ask what a reasonable engineer would think of when you say “digital system” and if you would need to clarify if time is discrete or not. I suspect in most cases if we don’t clarify that then discrete would be assumed and that it would generally be safe for us to do so. In the cases where time is not discrete, it should be clarified for the same reason. – Dan Boschen Jan 11 '23 at 20:34
1

I would add to the notion of discreteness that the discrete symbols encoding the data or signal should also be finite, or taking a limited number of values in some set called symbol dictionary or alphabet, made for instance of numbers/digits or letters.

Laurent Duval
  • 31,850
  • 3
  • 33
  • 101