# In digital systems do we discretize both time and magnitude or only time?

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. 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.

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.

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.

• 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
• 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

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

• Fundamentally speaking, what should be a Digital Signal be like? both axis discrete values or only x-axis? for eg: what should a digital sine wave be like? – Atanu Sarkar Jan 29 '18 at 16:05
• Generally, both. – pjc50 Jan 29 '18 at 16:31

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.

• 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
• 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
• 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
• 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
• 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. en.wikipedia.org/wiki/Signal – Mitu Raj Jan 29 '18 at 20:26