Analog and Digital; Continuous and Discrete

[scoutfai]

Is it possible to have the following signal:

1) Discrete and analog
2) Discrete and digital (I believe this one is true and very common in man made product)
3) Continuous and analog (I believe this one is also true and very common in nature)
4) Continuous and digital

If a picture of such signal (f(t) versus t, f(t) can be current or voltage, t being time) can be provided as an example will be very much appreciated.

My understanding is (I am not 100% sure is right or wrong), "analog and digital" is a concept independent from "continuous and discrete" signal. The criterion that determines whether a signal is continuous or discrete depends on the argument (usually time). If the signal (or the function) has output only at constant interval of time (k, 2k, 3k, ... ..., k=any time, could be 1s, 1.5s, 2.1s, etc), then it is a discrete signal. If the signal has output at any time (any real number throughout the real number line), then it is a continuous signal.

Whereas the criterion that determines whether a signal is analog or digital depends on its output ( f(t), could be current, voltage, intensity, etc). If the output can be expressed as one of the element of the set {n, 2n, 3n, 4n, ... ...} ( n=smallest output value, could be 1V, 2V, 1.11V, 2.378V, etc) , then the signal is a digital signal. If the output can take any real number, then it is a continuous signal.

Hence, as a consequence of my understanding, I deem that all four kind of signal I listed above can exist.

Nevertheless, I also heard people claims that if a signal is digital, it must be discrete; If a signal is analog, it must be continuous, etc. So obviously, to them, some of signal listed by me can never exist. I am aware that the problem is best answered by review on the formal definition of different kind of signal from standard textbook. But I find those description rather confusing to me. Thus if you can provide me a simple and straight forward answer to my question first and followed by some detail explanation will be very much appreciated.

Looking forward to hear your thoughts.

 

[Feldoh]

It's sort of complicated, but you've mostly got it right.

Discrete implies a domain which is a set of integers
Continuous implies a domain which is a set of real/complex numbers

Digital signals imply a range which is a set of integers
Analog signals imply a range which is a set of real/complex numbers

The reason that digital is associated with discrete signals is because computers can only take finite time signals which have a finite numbers of values. For example we can't sample a signal any faster than our computer can run. Actually it's more like half the speed of your computer, but it's not really relevant. Then when we read data we can only have a finite range of values because our computer's registers can only hold a certain number of bits as a value. For example if our computers registers can only hold 6 bits than we can only take on 2^6 = 64 different values.

 

[rbj]

i souped up your quote, just a little

Is it possible to have the following signal:

1) Discrete-time and analog
2) Discrete-time and digital (I believe this one is true and very common in man made product)
3) Continuous-time and analog (I believe this one is also true and very common in nature)
4) Continuous-time and digital

1) Charge Coupled Devices (CCD) a.k.a. "bucket brigade".
2) DSP
3) analog filters and systems
4) it's possible you could have such a system with a "flash" A/D and unclocked logic operating on it. strictly speaking, any unclocked logic circuit would pass as continuous-time and digital.

 

[sophiecentaur]

It is true to say that all signals are analogue (even paper with numbers written on it) and it is only the information that a signal carries that can be digital (so you could do arithmetical addition of two of these written numbers by turning the shapes into maths and then back again). In fact, I would say that it is only the source information or way the signal is treated subsequently that determines the digital or otherwise nature of the information. So a computer modem churns out digital data and the computer treats that data as digits but your ears might just 'hear' a slightly musical, burbly noise.

I'm not sure about No. 4 above except in as far as all practical digital signals are effectively this. It's true that the actual level of this signal would vary continuously but, then, so does every digital signal. Depending on the response of the channel, you might get absolutely any value at any given time (presumably you are not envisaging an 'ideal' boxcar waveform) and what started off as some set of discrete levels at some set of sampling times won't be like that any more. The information in this signal is not continuous - it is discrete in time.

 

[AlephZero]

A simple example of "continuous and digital" would be a digital signal with only one bit of information, and no clock. For example, a push-button switch, or a movement sensor triggering a security light.

Of course you could argue that the electrical signal here is "really" analog, but it is interpreted as a digital signal, for example by comparing it with some voltage threshold to decide if it is "on" or "off".

 

[sophiecentaur]

"continuous digital" is an oxymoron if, by digital, you mean discrete. At the transition (and you could look at any time) the value could be anything between 0 and 1 so which would you shoose? If the transition were instantaneous then the signal is not continuous.

But I think we agree it is really the information that is carried that makes a signal analogue or digital. The value of whatever variable is carrying digital information is actually analogue.

 

[rbj]

"continuous digital" is an oxymoron if, by digital, you mean discrete.

there is a difference between discrete-time and discrete-amplitude. generally, i think "digital" generally means discrete-amplitude.

conceptually you can have continuous-time and discrete-amplitude together, but it would be a sort of weird system.

 

[sophiecentaur]

Are you just referring to a set of asynchronous, quantised samples? The transitions between samples would not be quantised (discrete), though.
Imagine a set of numbers flashed up on a screen, there would always be a transition from one to another, either fading from one to another or fading to black OR discontinuous changes (not continuous).
btw, where is this going? ;-)

 

[rbj]

Are you just referring to a set of asynchronous, quantised samples?

not for continuous-time signals and systems. but that is an independent issue from discrete-amplitude (which i am equating to "digital").

The transitions between samples would not be quantised (discrete), though.
Imagine a set of numbers flashed up on a screen, there would always be a transition from one to another, either fading from one to another or fading to black OR discontinuous changes (not continuous).

well, to take it to an extreme, even digital circuits are analog. when a binary signal transitions from 0 to 1 there is a transition with a transition time. but the logic circuit receiving that signal makes a decision whether to interpret that signal as a 0 or 1. we don't know in advance precisely where that threshold will be (but we know the allowable range of that threshold), but that signal is always, from the POV of a receiver, a 0 or a 1, if it's binary logic.

now, you can have logic without there being a clock. it's not as common as logic with a clock synchronizing things, but it's possible and sometimes such logic circuits exist. a plausible (but i am not suggesting common) situation would be a flash A/D converter (there is no clock with that) connected to unclocked logic that does something with the output of that flash A/D (like converts it to 7-segment display). that would be an example of continuous-time and digital.

btw, where is this going? ;-)

i dunno.

i just wanted to confirm to the OP that Discrete (time) normally goes along with Digital, Continuous (time) normally goes along with Analog (as he/she suspected), but there are (or can be) exceptions to either.

 

[sophiecentaur]

Firstly, digital signals ARE Analog. But the information that is carried and used by them is digital. The distinction is between signal and information. Digital (discrete) information can't be 'in between' values but there has to be a certain fuzziness as one signal value changes to another. I guess I am defining a signal as some quantity that is used to transfer information, so what I am saying has to be true. But, if the definition is different then I'm not correct.
Synchronous logic is actually a 'modern' invention. Mechanical telephone exchanges were totally asynchronous and so was telegraphy and lift (elevator) controls.