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I'm trying to better understand the differences between analog, digital, continuous, and discrete signals in the context of signal processing. Here's what I've gathered so far, but I’d like some clarification:

What I Understand Analog vs. Digital:

These depend on the y-axis values of the signal: If the signal can take any value on the y-axis, it’s an analog signal. If the signal takes only specific values (e.g., 0 and 1), it’s a digital signal.

Continuous vs. Discrete:

These depend on the x-axis values: If the signal is defined for all points on the x-axis, it’s a continuous signal. If it’s only defined at specific points (e.g., integers), it’s a discrete signal. My Current Categorization Based on this, I think signals can be categorized as:

Continuous-Analog: Signals like sine waves where both x and y are continuous.

Continuous-Digital: Signals with continuous x-values but discrete y-values, like square waves.

Discrete-Digital: Signals where both x and y are discrete, such as a sampled digital signal.

I’ve noticed that many people equate:

Continuous signals = Analog and Discrete signals = Digital

(i think its not correct in general)

Is it possible to have a "Discrete-analog " signal?

For example, where the x-axis is discrete but the y-axis is continuous. If so, how would such a signal look in practice? Does my understanding of the categories seem accurate?

Are there any nuances I’m missing in how these types of signals are defined or classified? Thanks for your insights! I’d appreciate examples or corrections to my understanding. btw idk how to write question stack exchange so plz adjust. and help me to write questions in stack exchange .

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  • \$\begingroup\$ This is probably a better first for the signal processing stack exchange, but usually what you called "Discrete-Digital" is what most people would simply call "digital" since computers work with sampled and quantized data. \$\endgroup\$ Commented Dec 9, 2024 at 13:49
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    \$\begingroup\$ It’s important to realize that most of these are abstractions. As for “discrete-analog”, we typically see this abstraction when developing the theory/mathematics for ideal discrete time sampling where you multiply the analog signal with a uniformly spaced impulse train (Dirac comb). At this point you can treat the result as what you are calling “discrete-analog”. The following step of “quantization” is what makes the y-axis discrete and allows you realize this abstraction in a computer as a “digital” signal. \$\endgroup\$ Commented Dec 9, 2024 at 14:10
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    \$\begingroup\$ @user1850479 Indeed: dsp.stackexchange.com/questions/34465/… \$\endgroup\$ Commented Dec 9, 2024 at 17:07
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    \$\begingroup\$ These are vital general concepts: the most important thing to note is that not everybody uses the words in the identical way, and you need to pay good attention to context. \$\endgroup\$ Commented Dec 10, 2024 at 7:52
  • \$\begingroup\$ An example of discrete voltage with continuous time would be (some) pulse-width modulation, such as a signal for a servo. \$\endgroup\$ Commented Dec 10, 2024 at 7:57

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digital signals: These depend on the y-axis values of the signal: If the signal can take any value on the y-axis, it’s an analog signal. If the signal takes only specific values (e.g., 0 and 1), it’s a digital signal.

nope, that's just "value-discrete". Digital also requires "defined only at discrete points in time".

So, all physical signals outside quantum electronics (and even within, discrete-time is rare) are in fact analog. The way they get dealt with might be digital (i.e., only the values at discrete times matter, and these also get quantized).

Hence,

Continuous-Digital

is an oxymoron,

Continuous-Analog

is just "analog",

Discrete-Digital

is just "digital"

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    \$\begingroup\$ I would not say that a digital signal is "defined only at discrete points in time." I would say instead that the signal represents a sequence of measurements that were acquired at discrete points in time. Any requirements regarding the moments when the receiver of a real-time, digital signal is or is not allowed to look at it would come from, IMO, a protocol specification, and not from a general specification of what "digital" means. \$\endgroup\$ Commented Dec 9, 2024 at 15:25
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    \$\begingroup\$ Re, 'nope, that's just "value-discrete".' Also known as, "quantized." \$\endgroup\$ Commented Dec 9, 2024 at 15:26
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    \$\begingroup\$ @SolomonSlow I would definitely say what I said ;) Digital signal processing is concerned with the processing of digital signals (that's where I hence would take the definition from), and for us DSP folks, a signal is digital exactly when it's discrete in both time and value. \$\endgroup\$ Commented Dec 9, 2024 at 16:49
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    \$\begingroup\$ I don't disagree with that at all. I can't imagine any practical method of delivering a signal that could be called "digital" if the signal is not both sampled and quantized. \$\endgroup\$ Commented Dec 9, 2024 at 17:09
  • \$\begingroup\$ @MarcusMüller If the signal takes only specific values (e.g., 0 and 1) at every point in time, isn't that continuous-digital? \$\endgroup\$ Commented Dec 16, 2024 at 4:46
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A digital signal, sampled (discrete) and processed inside a processor or dedicated digital (binary) circuit is an abstraction. All signals are analog and continuous.

If you look at a transition from 0 to 1 at the voltage level, for example, the signal doesn't change from 0V to 5V instantly, so it has infinite levels at infinite times between these two levels.

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    \$\begingroup\$ The name, "digital signal," contains the word, "signal." If you want the world to agree that a digital signal is not a signal (All signals are analog), then I think that's a fight that you are going to lose. \$\endgroup\$ Commented Dec 9, 2024 at 15:23
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For a random continuous signal, the probability that the signal is exactly a given value is zero.

For a discrete signal, the probability that a uniform random signal is exactly a given legal value for that signal is 1/(the number of legal values)

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  • \$\begingroup\$ no, digital signals don't necessarily have uniform probability distribution. \$\endgroup\$ Commented Dec 9, 2024 at 17:19
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    \$\begingroup\$ @MarcusMüller -- they do when you specify that they do as I did here to make a statistical point. It's certainly not a requirement of a discrete signal, but it's certainly possible to generate a random discrete signal with a uniform distribution, and when you do, you know the (non-zero) probability that it takes on any given legal value. If the signal is random, but not uniform, there's still a non-zero probability, but with a different value. I never said or meant to imply that discrete signal must have a uniform distribution. They don't need to be random, either. \$\endgroup\$ Commented Dec 9, 2024 at 17:40
  • \$\begingroup\$ but it really doesn't work that way. You can have an continuous-valued signal with a distribution that is, say, 1 V in 50% of cases, and uniformly distributed between 0 and 2 V the other 50% of cases. \$\endgroup\$ Commented Dec 9, 2024 at 23:25
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    \$\begingroup\$ @MarcusMüller I confess I am completely missing your point. I made zero claims about the distribution of continuous signals other than random. If 50% of the values are 1.000000000, that isn't random. \$\endgroup\$ Commented Dec 10, 2024 at 0:31
  • \$\begingroup\$ How is "flip a coin; if tails 1V, if head uniform noise" not random! It definitely is random, and the accompanying probability density might not look like you like a function to look, but it's a valid random signal still. \$\endgroup\$ Commented Dec 10, 2024 at 9:24
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Analog

Look up "analog" in a dictionary some time. That word is older than electronics. An analog is any quantity that varies in proportion to some other quantity. When we talk about electronic analog signaling, we usually are talking about an arrangement where some voltage or some current or some frequency varies in proportion to some measured quantity such as the temperature or pressure at some point in a process or, to the level of liquid in a tank.

Discrete

"Discrete" can mean that only certain values of the measured quantity are recorded (also known as a quantized signal), but it can also mean that the value is only measured at certain moments in time (also known as a sampled signal.)

Digital

"Digital," is easy to understand. It refers to numbers. A digital signal is a sequence of numbers that represent how some quantity changes over time. If some communication means delivers a digital signal, that means that the first step in understanding it is to convert it to a sequence of numbers, and only then, can you understand those numbers as representing how some value changed over time.

Digital signals, in virtually all practical applications, are both sampled and quantized.

Is it possible to have a "Discrete-analog " signal?

Yes. See above. An analog signal can be quantized (only reports certain values of the measured quantity) or it can be sampled (the quantity is only measured at certain points in time) or it can be both.

For example, where the x-axis is discrete but the y-axis is continuous. If so, how would such a signal look in practice?

An analog signal that was sampled (x-axis is discrete) but not quantized (y-axis is continuous) might look like this:

Plot of sampled, but not quantized, analog signal

A signal like this could be the output of a "sample-and-hold" circuit that is the first stage in some types of analog-to-digital converters.

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    \$\begingroup\$ please, please please! don't draw digital signals as "sample and hold". This confuses so many students, and it is on contrast to how samping and reconstruction (of band-limited signals) work. \$\endgroup\$ Commented Dec 9, 2024 at 17:18
  • \$\begingroup\$ @MarcusMüller, I don't believe I said that the drawing represented a digital signal. I have changed the wording. I hope it makes my intent more clear. \$\endgroup\$ Commented Dec 9, 2024 at 17:30
  • \$\begingroup\$ "A signal like this could be the output of a "sample-and-hold" Does that mean that the signal has the same analog/continuous y value between the sampling points? \$\endgroup\$ Commented Dec 9, 2024 at 17:44
  • \$\begingroup\$ @MeGrogu, That's what "hold" means. When a sample-and-hold circuit is "sampling," its output (typically, output voltage) follows its input (voltage.) When it is "holding," the output freezes, and it remains constant, regardless of what the input is doing, until it's time for the next sample. \$\endgroup\$ Commented Dec 9, 2024 at 18:11

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