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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 Sep 27 '16 at 20:06
  • $\begingroup$ Any comparator might produce a continuous-time 1-bit Digital signal output. $\endgroup$ – hotpaw2 Sep 27 '16 at 20:29
  • $\begingroup$ @robertbristow-johnson I learned that "digital"=="time-discrete && value-discrete"! $\endgroup$ – Marcus Müller Sep 27 '16 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 Sep 28 '16 at 13:46
  • $\begingroup$ gray encoders (position encoders utilizing gray code) are by design continuous-time and digital :-) $\endgroup$ – Olli Niemitalo Oct 7 '16 at 12:14
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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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