# Discrete time signal with continuous output = analog system?

This was a bit of a topic of debate in my class today.

"A system measures the speed of the wind and provides voltage values proportional to the speed of the wind every 2 seconds."

Is this an analog system or digital?

I am calling this an analog system, based on several things. We have the fact that it's wind that's being measured (a very analog thing in nature). It's also not stated what type of system is used to measure this wind. But assuming the wind measurement is continuous, like some old analog pressure gauge, then the proportional voltage at the output should also be continuous. Meaning there are an infinite number of wind speeds, hence, and infinite number of voltages at the output (in theory). So an analog system,

This is also quite confusing because we're not told whether a computer is assigning those values, or just some guy eyeballing a pressure gauge. So I can't assume it's a computer. If it was a computer, it would obviously be a digital system.

Now, we had many colleagues assume that the system was digital, based solely on the fact that the measurements are taken every 2 seconds (a discrete time signal).

Now I would argue that if the voltage signal at the output was quantized, or rounded to a specific decimal, then yes, we would have a digital system.

• If the only piece of information given is that one sentence then it appears to be an analog system. Even if the output were produced by a DAC on a microcontroller I would be tempted to say that the system is still analog, because a DAC is a digital-to-analog converter. Once digital is converted to analog, it is not digital anymore (I would argue). Commented Sep 7, 2021 at 1:46
• Better to accept that everything is quantized. Stick a mercury thermometer into a hot bath and it's still a quantized measurement, jiggling here and there. Read this [translation of Boltzmann's "On the Relationship Between the Second Fundamental Theorem of the Mechanical Theory of Heat and Probability Calculations Regarding the Conditions for Thermal Equilibrium"](file:///C:/Users/Jon/AppData/Local/Temp/entropy-17-01971.pdf). (I think Shannon's two papers on information theory are clearer reading. But they also arrived decades later, too.) Move to single particles and it's still quantized.
– jonk
Commented Sep 7, 2021 at 4:57

This is an analog system.

A system measures the speed of the wind and provides voltage values proportional to the speed of the wind every 2 seconds.

The key word is "proportional". This means that if the voltage changes by a small amount the output also changes by a proportional amount. It implies there is no discretization of the output voltage.

A digital system is one in which the signal values are discretized (take only certain specified values). Since this system has signals that are proportional to a continuously varying quantity those signals are also continuously varying and the system is analog, not digital.

• These are exactly my thoughts because the input could be 3.56666666… or 6.7878787878… or anything in between. Infinity. And the output would be proportional to that, with no mention of quantization. A guy eyeballs an analog pressure gauge and picks a number to some random degree of accuracy. Then at the output we get the voltage number proportional to that. Looking around online it seems like there’s quite a bit of confusion and wrong information as to what a digital signal even is. Commented Sep 7, 2021 at 5:52

Sometimes the point of these assignments is to discuss the various reasons why something could be classified as something and why not, and there is no right answer. The system might be vaguely described for a reason to allow for either answer, based on how you look at it.

You said yourself the system is not clearly defined, so obviously you already made your answer based on your assumptions about the system and how it in your opinion is, so other people are allowed to do that as well.

You can have continous signals, and you can have discrete time signals, and they both can have analog or quantized values. Computers can also be analog, it's just rare these days.

As this is a hypothetical situation, there will be no definite answer whether the system in question is analog or digital. It could be either - it does not rule out that the analog signal could be quantized, it just says it's voltage output and proportional to speed.

• It's a multi-part question and in one of the parts the voltage is said to be quantized at the output. In that case I would say digital. I also agree that there doesn't seem to be a definitive answer here. That's really what i'm looking to confirm. Commented Sep 6, 2021 at 23:35
• @BobaJFET But if the assignment says the output is voltage, voltage is analog even if it is quantized, so the output itself can't be a digital. However the output might have been a digital number before a DAC converted it to analog. Commented Sep 6, 2021 at 23:42
• They use the word "value" for the voltage. So i'm assuming this is a number. I would also think that quantizing it would make it digital because now there's a finite number of values it can have. Commented Sep 6, 2021 at 23:45
• Yes, it could be a digital value representing voltage, sent over serial port or something. However, if it was a number in the first place, why would it be stated it is a voltage value to begin with? If you measure wind speed which gives a digital output in pulses or frequency based on wind speed, there is no reason to specify that value as any voltage, not unless the number it is converted to analog voltage with a DAC. Commented Sep 6, 2021 at 23:53

It’s a velocity value with a 2 second sample interval, represented as analog. Because it’s sampled, it would be considered a discrete time system. Is it digital? No, at least as described, even though the values aren’t continuous.

Don’t confuse discrete-time with digital - they’re not the same. A discrete time signal isn’t digital until it’s converted to some kind of pulse code modulation. But to be converted to PCM, it does have to be a sampled discrete-time signal, which is further quantized to a stream of digital values.

Provides Voltage Values means it's an analogue system.

That's taking the words at face value of course.

If somebody is arguing that the system could be providing numbers that measure those voltage values, that would be a digital system. But then the sentence would read 'provides numbers representing ...'

It is a sampled system. And these days, sampled is often used, incorrectly, as a synonym for 'digital'.

Back in the days before ADCs and DACs, engineers were using sampled analogue to solve problems, with all the attendant 'analogue' problems that have driven the world 99.whatever% digital. I came across one system from IIRC the 1970s which used analogue time division multiplexing to provide 32 zoned channels of audio into an airport public address system. Of course when the timing slipped, one zone's output would be the sum of it and the adjacent (on the multiplex) zone.

I don't know if I can help with your question, but I can certainly throw my hat into the ring. This is more an opinion piece than anything else.

I had this exact same debate with my students, once. The argument kicked off when one of the students asked if an analogue clock whose second hand "ticks" discretely from second to second can really be considered analogue.

I always accepted, before this debate, that analogue signals were continuously variable, with no discretisation. Similarly an analogue system was one in which all operations on those signals were continuous functions.

However, I had never given it much thought, and I was forced to redefine my understanding of what it meant to be "digital". In the sense that the clock's purpose was to display time in an analogue form, and that perhaps the "ticking second hand" was merely an artifact of the way the clock worked, I believe the class's consensus was that the clock should still be considered analogue.

It has become clear to me that it is not the physical nature of the signal or system that defines its "digitalness", rather it's the intended purpose or interpretation of the signal/system. It's also clear that it doesn't make sense to try and label all signals and systems as existing/operating exclusively in either the analogue or digital domain, since there exists a grey area in bewteen, like for instance when the intention is to derive a digital representation of some analogue property (or vice versa), a "conversion".

While it's clear that the signal being converted starts off as purely analogue, with all prior circuitry (signal conditioning) also residing in the analogue domain, and it's clear that eventually there exists an unambigously digital form of that information, following which all processing takes place in an unambiguously digital regime, there exist intermediate forms of the information/signal which don't fit exclusively into either camp.

So I am now of the opinion that:

• the black and white pigeon-holing of signals and systems as either analogue or digital is flawed. Maybe we need a term like "digilogue" for those hybrid, intermediate states. Is there already such a term? An example would be the use of an analogue comparator to regenerate a heavily attenuated digital signal. Which system is it, analogue or digital?

• such categorisation should not be based on physical attributes of some property/signal/system, but rather upon the interpretation of the property, or the intended regime of operation of the system. Temperature is clearly an analogue value, not because it is continuously variable, but because we perceive and understand it so. A digital audio signal is not digital because it consists of a physical voltage changing between 0V and 5V, but because we interpret and operate upon that data in a digital context. The distinction between physical manifestation and purpose/interpretation is subtle, but important, I believe.

All that said, in the absence of some formal corroboration for my thoughts on this, and if it's absolutely necessary to label something as either analogue or digital, I would say that the system you described is analogue, and here's why:

Up to the point where a signal becomes unambiguously digital, whenceforth all operations are boolean in nature, prior ciruitry is dealing with voltages and currents in a very analogue sense, with attenuators and amplifiers and level shifters and all manner of not-quite-digital-yet stages. By this argument I am stating that if a signal is not completely binary, and ready to proceed into the realm of boolean logic, it's analogue, and the stuff that's conditioning it is also analogue.

I don't necessarily like this black/white pigeon-holing, but it's as close as I can get to a boolean choice between one or the other.