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In studies of Digital Circuits or Digital Electronics or Digital Systems, the very first step is to convert an Analog signal / Analog system into a Digital Signal / System.

Analog to Digital Convertion

In this process of converting an Analog function to a Digital Function, do we need to discretize both time (X-axis) and magnitude/functional value (Y-axis) or only time (X-axis)?

Can anyone give me the correct definition of this (Discretization / Analog to Digital Conversion), as I found at some places it says both time and value (both X-axis and Y-axis) i.e take (X,Y) ∈ ℕ, whereas at other places it says only time/X-axis values i.e only X ∈ ℕ and Y can have any values i.e Y ∈ ℝ.

Atanu Sarkar
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An analog signal that is sampled is called a discrete-time signal.

An analog signal that is quantized is a discrete-valued signal.

A signal that is discrete in time and amplitude is called a digital signal.

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Mario
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The answer depends on what you are doing.

A sample and hold circuit will sample the analog signal at discrete time points, hence converting to digital in only the time (X) axis.

An analog-to-digital converter will sample the magnitude at discrete time points, hence converting to digital in both time (X) and magnitude (Y). This is the most useful form of a digital signal, which you can process in a digital signal processor or FPGA.

OneOf6inMD
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  • Fundamentally speaking, what should be a Digital Signal be like? both axis discrete values or only x-axis? – Atanu Sarkar Jan 29 '18 at 16:06
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    Both situations will arise but it is far more common for both to be discretised, which is necessary for the majority of digital signal processing. – loudnoises Jan 29 '18 at 16:25
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Both. An analogue-to-digital converter usually emits a series of quantized values, each of which represents the value of the input at a particular time. Usually they are sampled regularly at a particular sampling rate.

To complicate matters slightly, there are types of ADC which ouput discrete digital values but are continuous in the time domain: http://www.electronicdesign.com/analog/what-s-difference-between-continuous-time-and-discrete-time-delta-sigma-adcs

pjc50
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A discrete time signal can be called as a digital signal when its amplitude is made discrete too. i.e., when the amplitude is quantised. In ADCs, it does both sampling and quantisation. Means, the analog signal is made discrete in both amplitude as well as time axes.

Mitu Raj
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  • Okay, so a "*Digital Signal*" and a "*Discrete-time signal*" is **NOT** exactly same, and also a "*Analog Signal*" and a "*Continuous-time signal*" is **NOT** exactly same. **Analog**: Neither time nor amp is quantised. (X,Y) ∈ ℝ **Continuous-time**: Time axis is not quantised. X ∈ ℝ **Digital**: Both time and amp are quantised. (X,Y) ∈ ℕ **Discrete**: At least time must be quantised. X ∈ ℕ [am I right ??] – Atanu Sarkar Jan 29 '18 at 19:19
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    Discrete time signal means time is discrete. Its amplitude may be continuous or discrete. Continuous time signal means time should be continuous. Its amplitude may be continuous or discrete. – Mitu Raj Jan 29 '18 at 19:32
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    Digital signal means its quantised or discrete in amplitude. Its time axis is not necessarily discrete. It can be continuous too. eg. square wave signal. Analog signal means its amplitude is not quantised, it is continuous. Its time axis may be discrete or continuous. – Mitu Raj Jan 29 '18 at 19:34
  • so can I conclude by saying: | Analog Signal: Both time and amp is continuous and none is quantised, i.e (X,Y) ∈ ℝ | Continuous-time Signal: Time is continuous and not quantised, i.e X ∈ ℝ | Digital Signal: Both time and amp should be quantised, i.e (X,Y) ∈ ℕ | Discrete-time Signal: Time should be quantised, i.e X ∈ ℕ (*"Every Digital Signal is a Discrete-time signal and Every Analog Signal is a Continuous-time Signal, but not the other way round !"*) – Atanu Sarkar Jan 29 '18 at 19:39
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    Cant really say " All digital signals are discrete in time". Eg. A continuous square wave toggling 0 and 1 is considered as a digital signal but its not discrete in time. – Mitu Raj Jan 29 '18 at 19:42
  • Analog can be discrete in time too. So its not necessary that all analog signals are continuous time signals. However typically we are interested in analog signals which are both continuous in time and amplitude. hence the terms are interchangeably used in most books. – Mitu Raj Jan 29 '18 at 20:02
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    You just need to think like this to avoid confusion: Analog and Digital signals --> differentiated based on Amplitude only. Discrete and Continuous time signals --> differentiated based on based on Time only. – Mitu Raj Jan 29 '18 at 20:04
  • The "Discrete and Continuous **time** signals" part is clearly well understood. Can you provide links to some books/sites where "Analog and Digital signals --> **differentiated based on Amplitude only and not on time**" is clearly stated, described and defined. – Atanu Sarkar Jan 29 '18 at 20:10
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    When we talk about analog and digital, we are interested in only about how their amplitudes are represented, not about time. However when it comes to analog signals, continuous time domain is more relevantly used. https://en.wikipedia.org/wiki/Signal – Mitu Raj Jan 29 '18 at 20:26
  • Good explanation here --> https://en.wikipedia.org/wiki/Digital_signal -- in DSP domain, digital signal is considered discrete both in time and amplitude.While in digital systems and communications systems, digital signal can be continuous in time too. eg. PAM signal – Mitu Raj Jan 29 '18 at 21:09