Analog Signal of Noncontinuous Variables

[Puglife]

In my electrical engineering Textbook, In the beginning of it, when they were introducing analog and digit signals, they said an analog signal was a signal that depends on some sort of changing continuous variable such as time.

The later went on to say that Analog signals can be depending on noncontinuous variables, but did not give an example, and just left it as that one sentence.

I was wondering if anyone could give me an example of such a wave, or if the textbook simply had a typo.

Thank You

 

[anorlunda]

An example of noncontinuous is an on/off switch.

 

[Puglife]

An example of noncontinuous is an on/off switch.

wouldnt an on off switch be digital though?

 

[anorlunda]

Lol, give me your definition of analog and digital.How about lightning? There must be an infinite number of examples.

 

[Puglife]

Lol, give me your definition of analog and digital.How about lightning? There must be an infinite number of examples.

Digital would be any signal that has a non continuous set of states, such as a square wave, which is either at full amplitude, or zero. Is that not the definition of a digital signal?

 

[anorlunda]

In that case, you have boxed yourself into a corner with contradictory language. You want an example of a non -continuous continuous signal.

Your question has nothing to do with physics, just use of language.

 

[Puglife]

In that case, you have boxed yourself into a corner with contradictory language. You want an example of a non -continuous continuous signal.

Your question has nothing to do with physics, just use of language.

So do all analog signals depend on continuous signals? Cause the textbook said they don't, and gave me that exact definition for a digital signal. I am assuming their was just a typo in the textbook then.

 

[anorlunda]

Textbook authors can also abuse language. What does your common sense say?

 

[Puglife]

Textbook authors can also abuse language. What does your common sense say?

that they are wrong, that's why I went to the forum in the first place, to confirm or deny that with certainty. So they are wrong then?

 

[anorlunda]

does the book also say that analog and digital are mutually exclusive? Could you look at a digital circuit from an analog viewpoint? Can a circuit have some analog and some digital components?

Natural language is necessarily imprecise, physics is not. Your focus should be on the physics.

 

[Puglife]

does the book also say that analog and digital are mutually exclusive? Could you look at a digital circuit from an analog viewpoint? Can a circuit have some analog and some digital components?

Natural language is necessarily imprecise, physics is not. Your focus should be on the physics.

ok, I was just making sure that my understanding of the physics was not compromised by their strange wording.

 

[tech99]

ok, I was just making sure that my understanding of the physics was not compromised by their strange wording.

Maybe the book is referring to a signalling scheme such as pulse width modulation, which is discontinuous but represents an analogue signal.

 

[sophiecentaur]

Can a circuit have some analog and some digital components?

Aye, that is the question.
There is really no such thing as a "Digital Component". Anything that you can make, works in an analogue fashion.
The fact is that anything you can measure is analogue and it is part of a continuous signal (however fast you may try to switch the state on and off). The Digital Content of an analogue signal is what people, who are being customarily sloppy, mean by a Digital Signal. The state of an analogue signal at some chosen time ( say in the middle of the elements in a binary bit stream) is what carries the Digital Information.
The big problem is how Digital and Analogue are described in our early tuition. The familiar 'boxcar' waveform is an idealised analogue signal in which the digital states are easy to identify because the analogue signal spends a long time at a '1' or a '0'. Real signals, carrying digital information over a significant distance are not boxcar. If the are then someone should sack the engineer / designer of the link. Real 'digital' signals. on a channel that is working to capacity, consist of 'wavy lines' with significant inter-symbol interference at most points in the waveform. See this link for an idea about how real signals behave.
I could suggest that the OP was not well served by what has been read in the textbook. Perhaps there is more to be read, elsewhere in the book which could put him / her right about the distinction between the types of signal. Digital Information is always carried by an Analogue Signal (even when that signal consists of handwritten characters, on a page.)

 

[FactChecker]

I don't like the textbook distinction between "analog" and "discrete". I think it is more normal to distinguish between "continuous" and "discrete" and also between "analog" and "digital".

It is normal to distinguish between continuous and discrete signals on an analog signal line. The continuous signal values are directly related to the level of voltage, current, frequency, etc. on the line. The discrete signals take specific, discrete, values matched to certain signal ranges on the line. Often, they are 0,1 values depending on the signal level being less or more than half the signal range.

It is also normal to distinguish between analog and digital signals. Analog signals can transmit information in the form of voltage levels, current levels, frequencies, etc. at one instance of time. Digital signals transmit information in the form of groups of 0,1 bits to represent numerical values. Digital signals can have a separate wire for each bit or it can send a series of bits on one wire in some small amount of time.

 

[sophiecentaur]

We are almost in agreement but I would say, rather, that a 'signal' is the value of a continuous variable and that it is possible to carry digital (discrete) 'information' on an analogue signal. If you receive a signal with a receiver of some sort, all you will know is that a voltage ( or current) is varying in time. If you know that the signal consists a carrier that is modulated (and coded) in some way, then by demodulating and decoding it in some way, you can get digital information from that signal.
The popular assumption that a 'digital' signal consists of a string of ones and zeros is really far too simple and excludes all the other ways in which digital information is coded and carried. Binary is only a subset of digital information coding.
An oscilloscope trace which consists of a set of voltage values that alternate between 2 V and 0V in some apparent order is not a 'digital signal' until someone tells you, firstly that it is actually carrying digital information and secondly how to extract the information. Without that side information, the trace could be telling you the brightness of the slats on an uneven picket fence and the analogue waveform values at the transitions could in fact be the important information on the signal.

 

[leright]

a digital signal is a signal that can have discrete values. An analog signal is a signal that can have a continuous range of values. These values could be voltages, currents, frequency, phase, etc. A digital signal NEED NOT have only two values, like in a modern binary computer. It can have any number of discrete values. There have been attempts to build three or more (voltage) level logic systems as well. However, the more levels you have the less noise immunity you have.

Also, real binary digital signals, as mentioned above, are not perfect square shaped signals since practical channels over which data is communicated have finite bandwidths.

 

[sophiecentaur]

Also, real binary digital signals, as mentioned above, are not perfect square shaped signals

Exactly. The digital values / symbols are carried on an analogue signal ( a varying voltage / carrier level / carrier phase etc).
Without making this kind of distinction, you can end up talking in terms of "filtering" a digital signal when the analogue signal is passed through an analogue filter. To filter digital information, you need a digital process, which is done in a logic circuit after the digital information has been extracted from the analogue signal.
I realized that common terminology is not so strict but why not try, on a forum like PF, to use less approximate descriptions. If we don't then who will?
PS We don't want to be like the people who claim to have a "Satellite" on their wall.

 

[FactChecker]

Exactly. The digital values / symbols are carried on an analogue signal ( a varying voltage / carrier level / carrier phase etc).
Without making this kind of distinction, you can end up talking in terms of "filtering" a digital signal when the analogue signal is passed through an analogue filter. To filter digital information, you need a digital process, which is done in a logic circuit after the digital information has been extracted from the analogue signal.
I realized that common terminology is not so strict but why not try, on a forum like PF, to use less approximate descriptions. If we don't then who will?

We don't want to cause more confusion than the OP asked for. Without getting into the details of the transmission method, there are signals that are commonly called "digital". They are quite different from the signals that are commonly called "analog". Details about different digital buses, RS232, 1553, etc are not called for here. There are many switch high/low signals that are sent on normal analog lines with no digital communication protocol. I would not call them digital signals. I would call them discrete signals.

 

[sophiecentaur]

I approve of the term "discrete".

 

[the_emi_guy]

I am thinking that the OPs "Analog signals can be depending on noncontinuous variables" may have been referring to something like a signal such as:
f(t) = 0 for t < 0
f(t) = 1 for t = 0
f(t) = e^-t for t > 0

This is clearly not digitally encoded due to the exponential tail, but has a non-continuous point at t=0

 

[analogdesign]

I think some of you guys (not all) are missing the point of the statement of the textbook. It has nothing to do with "digital is really a special case of analog" or "digital rides on an analog wave" or whatever. Even in an idealized world, there is an important subclass of signals called "discrete-time analog" which is a practical example of a non-continuous analog circuit. I have based my career on them.

Basically a discrete-time analog signal is a signal that has been sampled, but not digitized. That is, it is discrete in the time domain (meaning, simply, that it is only defined at the sampling instances) but it is continuous in the amplitude domain.

For example, if you sample a 10 Hz sine wave that various between 1 and 2V at 100 MHz, you would have a lot of samples with all values between 1 and 2V (for example, 1.302V will show up somewhere) but they are only valid every 10 ns (multiples of the sampling period). But it is only sampled, not digitized. So you don't have a 16-bit number that represents 1.302V for instance, you actually have a voltage of 1.302 sitting on a capacitor.

If you've ever heard of "switched-capacitor" circuits that is what they are doing. Switched-capacitor circuits are discrete-time analog circuits... kind of an interesting purgatory between analog and digital. Often it is an early step in the digitization process but it doesn't have to be.

As an interesting aside, discrete-time signals aren't the only non-continuous analog signal. Another example is pulse-width modulation (when that modulation embodies analog information).

 

[iVenky]

All physical voltages are analog only. Even if they are 1s and 0s, because you are finally going to represent it with some voltage levels like +0.9 V for 1 and 0 V or 0 or it could also be +0.9V for 1 and -0.9V for 0. So these physical voltages are analog only. Now, the thing is, you can do all the operations from an higher level of abstraction by converting these to 1s and 0s, which makes the math easier and also helps in compatibility with other voltages since you are just dealing with just 1s and 0s (and not 0.9 V or some other voltage level). Those operations are digital and are one level above the analog layer of abstraction.

 

[sophiecentaur]

I am thinking that the OPs "Analog signals can be depending on noncontinuous variables" may have been referring to something like a signal such as:
f(t) = 0 for t < 0
f(t) = 1 for t = 0
f(t) = e^-t for t > 0

This is clearly not digitally encoded due to the exponential tail, but has a non-continuous point at t=0

That is not a 'signal'. It is a Mathematical function. Any signal must be a continuous variation of some variable (all its variables, in fact). Transitions all take time and no real signal can have discrete values.

 

[sophiecentaur]

I think some of you guys (not all) are missing the point of the statement of the textbook. It has nothing to do with "digital is really a special case of analog" or "digital rides on an analog wave" or whatever. Even in an idealized world, there is an important subclass of signals called "discrete-time analog" which is a practical example of a non-continuous analog circuit. I have based my career on them.

Basically a discrete-time analog signal is a signal that has been sampled, but not digitized. That is, it is discrete in the time domain (meaning, simply, that it is only defined at the sampling instances) but it is continuous in the amplitude domain.

For example, if you sample a 10 Hz sine wave that various between 1 and 2V at 100 MHz, you would have a lot of samples with all values between 1 and 2V (for example, 1.302V will show up somewhere) but they are only valid every 10 ns (multiples of the sampling period). But it is only sampled, not digitized. So you don't have a 16-bit number that represents 1.302V for instance, you actually have a voltage of 1.302 sitting on a capacitor.

If you've ever heard of "switched-capacitor" circuits that is what they are doing. Switched-capacitor circuits are discrete-time analog circuits... kind of an interesting purgatory between analog and digital. Often it is an early step in the digitization process but it doesn't have to be.

As an interesting aside, discrete-time signals aren't the only non-continuous analog signal. Another example is pulse-width modulation (when that modulation embodies analog information).

There is an important step between the analogue signal and its 'discrete value. That is the Quantisation decision - chosing a time to sample and committing the input signal value to an 'agreed' discrete value bracket (which element of the constellation of values that is being carried). After that cleanup operation, you can assume safely that the samples values can be treated as discrete.
pulse-width modulation is subject to amplitude and phase noise so the 'value' that it carries is not discrete until it has been quantised appropriately. The numbers are discrete but they are not [Edit: directly] part of the analogue signal that carries them.

 

[the_emi_guy]

That is not a 'signal'. It is a Mathematical function. Any signal must be a continuous variation of some variable (all its variables, in fact). Transitions all take time and no real signal can have discrete values.

Agreed, but I think the OP is referring to the types of signals presented in his/her electrical engineering textbook, which are of necessity idealized versions of reality.

 

[sophiecentaur]

Agreed, but I think the OP is referring to the types of signals presented in his/her electrical engineering textbook, which are of necessity idealized versions of reality.

That's the fault of the textbook having a too trivial approach, I think. There are many books that limit their illustration of 'digital' signals to a simple box car waveform. Really not helpful if a student needs to take things further. And surely the purpose of Q and A on PF is to help spread a bit better information.

 

[analogdesign]

There is an important step between the analogue signal and its 'discrete value. That is the Quantisation decision - chosing a time to sample and committing the input signal value to an 'agreed' discrete value bracket (which element of the constellation of values that is being carried). After that cleanup operation, you can assume safely that the samples values can be treated as discrete.

This is true, but many analog signal processing systems are implemented in discrete time without quantization. I think this is what the original textbook was alluding to. They are less common now than they once were but many telephone circuits, for instance, would you discrete-time analog filtering. You sample a continuous-time signal, filter it using a switched-capacitor discrete-time filter, and then return it continuous time by applying the discrete-time signal to a continuous-time RC filter. No ADC, DAC, or digital processing required, yet it is most assuredly discrete time.

 

[sophiecentaur]

many analog signal processing systems are implemented in discrete time

I think we must be having a problem with terminology.
I can't think what you really mean by that expression. I guess that you mean they are sampled I agree that sampling, of course, does not mean either quantisation or digital coding. The resulting signal - a string of samples - is still analogue, continuous and its voltage values are no more 'discrete' than the original signal values. They vary smoothly from sample value to the next sample value. A reason for using a string of samples is to allow processes such as temporal filtering and the act of sampling re-jigs the spectrum to take artefacts away from the wanted spectral range. Another reason is to allow interleaving (time multiplexing) of many low frequency audio signals and producing a high bandwidth analogue signal for transmission. That signal is, of course, continuous.
The 'discrete' times you refer to will often be 'regular' not be instantaneous. This is partly due to the impossibility of actually realising this and also to the fact that the resulting signal noise will be worse than using longer sampling periods (= narrowing the bandwidth due to time integration). The sample waveform would be, for example a raised Cosine.
When demultiplexed, the component signals will be subject to the equivalent to inter symbol interference and, because they are not quantised, there is no way to 'wipe off' the spurious signals.
I cannot see how any of that process involves non continuous signals. The signal voltage values just have to vary continuously and the epochs during which they are being sampled are also continuous - i.e. the sample pulses have to be continuous functions too.

 

[analogdesign]

I think we must be having a problem with terminology.
I can't think what you really mean by that expression.

I think the terminology is what is the issue.

What i mean is that the *information* is discrete-time and so what the actual waveform is doing in-between samples is not relevant.

Take, for instance, an image sensor (it can be a CCD or a CMOS pixel sensor). As you read out the values you get a voltage proportional to the light incident on each pixel on it is settled. But the behavior of the signal while settling is completely and utterly immaterial. It can slew, jump up to 10V, ring like hell, it doesn't matter one iota as long as it settles to the final value within a clock period. It is only at the falling edges of this clock, for instance, that the signal (from a mathematical standpoint) is defined.

This is distinct from, say, an audio signal (unless it is sampled audio). If you are playing a musical tone and your opamp slews and glitches every microsecond you would hear it in your speakers. If you have a sampled audio stream (not quantized, just sampled) then you wouldn't notice the slewing behavior or the glitches. They simply wouldn't be part of the signal that reaches the speaker (assuming the reconstruction filter is linear).

You can express a discrete-time analog signal as a stem plot (or a train of impulses, if you like). It is undefined in between these points. Of course, in the real world, the waveform is doing something but that is not part of the signal.

 

[sophiecentaur]

Well, that's a relief.
I guess I would refer to what you're talking about would be something like 'Time- windowed sampling'. But at least we basically agree and we aren't getting into a fight about it.

 

[analogdesign]

Well, that's a relief.
I guess I would refer to what you're talking about would be something like 'Time- windowed sampling'. But at least we basically agree and we aren't getting into a fight about it.

I did get the sense we agreed, even if we didn't know it yet. ;)

I think "time-windowed sampling" would be a fine way to describe this kind of signal. I use the term "discrete-time analog" primarily because that is the term used in the analog IC business (these kinds are systems are almost always integrated). Since the OP is a student it is good to at least start by using generally accepted terms whenever possible.