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Are these terms just parallel words? If not, why is it that when one reads about the first then one is very likely to come across the second? In such case, what would be a nice example to explain the possible connection between the words?

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The word discrete is used to define a signal that is not continuous, but is composed of a sequence of values.

The word digital is used to define a discrete signal whose values have been quantized and can be stored... digitally.

You can have a discrete signal that is not digital, for example the signal $x = {\{1.002, \pi, 10.333\}}$ is a discrete signal that is not digital because $\pi$ is an irrational number that cannot be exactly represented in binary.

There is a subtle difference that is argued about by some people, but for almost any situation, the terms digital and discrete can be used synonymously when talking about signals.

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There is continuous time, and discrete time. With a continuous time signal, between any two points in time you can find signal, which may be different than either of the two points. With discrete time, there are values between certain points in time, and nothing between adjacent values. "Digital" is simply an additional quality. It's a convenient way to store individual values, so it's almost solely associated with discrete time.

"Samples" implies discrete time. But you can sample in the analog domain and stay there. For instance, there are analog delay lines using a "Bucket Brigade Device" (BBD) or "Charge Coupled Device" (CCD), where voltage values are held for a time—similar to holding a charge on a capacitor. But it's difficult to store those values permanently, and they tend to degrade quickly. So, it's simply easier to change each value to a digital value. Not only is there no degradation, and storage becomes relatively easy, but it's easier to do complex calculations without building increasingly complex analog hardware to do it. And once converted to digital values, we can exercise arbitrary precision, and there is no concern for environmental electrical noise.

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    $\begingroup$ I barely have any knowledge in SP but I recon from your answer that every digital signal is necessarily a discrete signal but any discrete signal is not necessarily a digital signal. $\endgroup$
    – Semo
    Aug 17 at 8:39
  • $\begingroup$ One could design a suitably perverse digital system that had continuous-time digital values (it would involve grey code, and probably glitches). But it's the kind of thing you'd do to win a silly bet, not something you'd do to actually apply to a real-world problem. $\endgroup$
    – TimWescott
    Aug 17 at 15:09
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Theoretically, it is easy to analyze a discrete signal only in variable.

A digital signal is discrete in both variable and value, which is the case in practical digital processing systems, such as DSP/CPU/FPGA etc.

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