Discretization of systems.

Signal: A function of a several dependent variables to a independent fixed variable (mostly time).

Two types of signals: Continuous and Discrete.

Continuous signals are the ones which has values at any given point of time. 

Continuous time control systems: Simple. In continuous time control systems, all the system variables are continuous signals. Whether the system is linear or nonlinear, all variables are continuously present and therefore known (available) at all times. A typical continuous time control system is shown in Figure below.

Discrete signals are the ones which exists only in discrete samples of time. You may not find any signal at points where the signal is not sampled. 

Discrete time Control System: Discrete time control systems are control systems in which one or more variables can change only at discrete instants of time. These instants, which may be denoted by kT(k=0,1,2,…) specify the times at which some physical measurement is performed or the times at which the memory of a digital computer is read out. 

So why do we need to discretize a system? Or What is the need for discretization of a continuous signal?

Discretization is carried out to shape a Continuous signal in such a manner which the controller can understand. This is carried out so that we can easily represent the signal in mathematical format and feed it to a controller to take required action. 

Continuous time control systems whose signals are continuous in time are described by

differential equation, whereas discrete control systems that involve sampled data signals or

digital signals.

So there are two processes involved in converting Continuous time system to Discrete time systems.

(1) Sampling 

(2) Quantization 

To be continued in the next Article of Sampling, Quantization using Zero order hold....