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I know that discrete signals have finite precision. But does that means that those signals can have only integer values(for example,2,3,4 etc) but not decimal values(for example 2.1,3.2,4.2 etc)?

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  • $\begingroup$ Just to complement the answer below: Discretized values are also called "digital". After sampling a continuous time signal, the signal is discrete time and after digitizing (or discretizing the values) the signal is called digital $\endgroup$
    – Engineer
    Apr 20 '20 at 21:48
  • $\begingroup$ "after digitizing (or discretizing the values)" what do you mean here? do you mean altering/adapting yaxis(amplitude) value or do you mean xaxis(time) value? $\endgroup$
    – engr
    Apr 21 '20 at 9:07
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    $\begingroup$ Discretizing the amplitudes (y-axis) $\endgroup$
    – Engineer
    Apr 21 '20 at 13:43
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There might be a confusion in the discreteness.

It can apply to the ordinal variable of the data: time for signals, space for images. Here discrete is the opposite of continuous. Which is not often well-defined. A common way is to consider that samples are finite in quantity, or enumerable: you can index them in $\mathbb{Z}$. For irregularly-sampled signal, we are in a borderline case. For instance, a classically discrete signal $x[n]$, $n\in\mathbb{Z}$ is considered discrete (in time). But their values (the quantities attached to $x[n]$) might be continuous in nature, e.g. $\mathbb{R}$. This is generally the context of the standard linear signal processing processing (because quantization is typically non-linear).

Then, a signal or, continuous or not in time or space, might have discrete, or discretized values (related to quantization). The values can be classical amplitudes, letters, or categories (oranges, apples, strawberries). Classically, practical real-valued signals have bounded amplutude or magnitude. So they often take values in a finite set or a finite field (in communications): $[0,\ldots,2^b-1]$, $[-2^{b-1},\ldots,2^{b-1}-1]$. Yet, even with IEEE floating-point, values remain discrete, because they are finitely many.

So, I suspect that for most, a fully discrete signal would have equally-spaced time samples, and finitely equally-spaced values (potentially with a compander).

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  • $\begingroup$ "For instance, a classicaly discrete signal x[n], n∈Z is considered discrete (in time). But their values might be continuous, e.g. R." what do you mean by values?y-axis(ampltude) values? $\endgroup$
    – engr
    Apr 21 '20 at 9:09
  • $\begingroup$ "a classicaly discrete signal x[n], n∈Z" here it appears that you are implying that for a signal to be discrete,its continous time version is sampled at integer value of time. Does that means, sampled at non integer(decimal) values of time ,will not be considered discrete? $\endgroup$
    – engr
    Apr 21 '20 at 9:12
  • $\begingroup$ "They are not always amplitudes (they could be categories, letters)" but generally those value are amplitude?Doesn't they?consider example of a sine wave of power signal $\endgroup$
    – engr
    Apr 21 '20 at 9:25
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    $\begingroup$ I've update the answer, hoping I did not forget something. Thanks for the comments $\endgroup$ Apr 21 '20 at 12:00
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They can very well have decimal values, represented as either fixed point or floating point numbers.

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