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It's my first time studying DSP and I've faced a problem finding a convenient definition.

Are the following definitions correct? And if so why there are some resources defining it in other terms such as "Digital signal: is a signal with discrete time and discrete amplitude"

  1. Discrete time signal: X-axis (time) is discrete and Y-axis (amplitude) may be continuous or discrete.

  2. Continuous time signal: X-axis (time) is continuous and Y-axis (amplitude) may be continuous or discrete.

  3. Digital signal: Y-axis (amplitude) is discrete and X-axis (time) may be continuous or discrete.

  4. Analog signal: Y-axis (amplitude) is continuous and X-axis (time) may be continuous or discrete.

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  • $\begingroup$ that's pretty much correct. in fact, relatively few Analog Signal Processors are discrete time (CCD is the exception). and i don't know any continuous-time Digital signals except for the output of a flash A/D converter. $\endgroup$
    – robert bristow-johnson
    Commented Sep 27, 2016 at 20:06
  • $\begingroup$ Any comparator might produce a continuous-time 1-bit Digital signal output. $\endgroup$
    – hotpaw2
    Commented Sep 27, 2016 at 20:29
  • $\begingroup$ @robertbristow-johnson I learned that "digital"=="time-discrete && value-discrete"! $\endgroup$
    – Marcus Müller
    Commented Sep 27, 2016 at 23:20
  • $\begingroup$ @MarcusMüller i am not sure that it absolutely must be discrete time. but other than a flash A/D (which has a "thermometer code" output word and no clock), i dunno anything else digital that is not discrete time. as hotpaw points out, a comparator outputs a 1-bit digital signal and it is continuous time. a comparator is a 1-bit flash A/D. $\endgroup$
    – robert bristow-johnson
    Commented Sep 28, 2016 at 13:46
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    $\begingroup$ @robertbristow-johnson: If you take several of those continuous-time (asynchronous) digital signals and feed them to combinatorial logic (like an OR gate), the output is also continuous-time digital. $\endgroup$
    – Ben Voigt
    Commented Jan 11, 2023 at 19:51

1 Answer 1

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A signal is indeed a function. Given a signal $f(x)$, according to whether continuous or discrete for both the variable $x$ and the function $f(x)$, there are four types of combinations:

(1) $\mathbf{continuous}$ $x$ and $\mathbf{continuous}$ $f(x)$

This is the most common $\mathbf{analog}$ signal.

(2) $\mathbf{continuous}$ $x$ and $\mathbf{discrete}$ $f(x)$

For this one, we can imagine the ideal base-band waveform used in digital communication. As this one: enter image description here

(3) $\mathbf{discrete}$ $x$ and $\mathbf{continuous}$ $f(x)$

This is indeed the signal in most the "digital signal processing" textbooks. An example, as others have pointed out, is the output of the CCD sensor.

(4) $\mathbf{discrete}$ $x$ and $\mathbf{discrete}$ $f(x)$

This is the $\mathbf{digital}$ signal. Digital signals are used in practical implementation aspects, and they actually exist in a conceptual manner.

If we concern the discrete feature of the function, the problem will be more complex, therefore, in most "digital signal processing" textbooks, the signals are $\mathbf{not}$ digital indeed. An interesting fact is that, for the the classical textbook by A. V. Oppenheim, the name was "digital signal processing" in the 1st edition, but the name was changed to "discrete-time signal processing" for the later editions.

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  • $\begingroup$ Your example of case (2) continuous $x$ (actually $t$) and discrete $f(x)$ ($f(t)$) actually falls into case (4). A better example of case (2) would be the output of an ideal pushbutton, photodetector, or comparator IC $\endgroup$
    – Ben Voigt
    Commented Jan 11, 2023 at 20:01

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