Signals and Systems: Classification of Systems

What is a System?

In signals and systems, a system can be defined in a number of ways as −

• A system is defined as a physical device that can produce an output or response for the given input.

• A system may also be defined as an entity which works on an input signal and transforms it into an output signal.

• A system can also be defined as a set of elements which are connected together and generates an output signal corresponding to an input signal.

Generally, a system is represented by a block diagram as shown in Figure-1. Here, the arrow entering the box denotes the input signal or excitation [r(t)] and the arrow leaving the box denotes the output signal or response [c(t)].

The relationship between the input signal r(t) and the output signal c(t) of a system is given as

𝑐(𝑡) = 𝑇[𝑥(𝑡)]

The output or response of the system depends upon the transfer function of the system. The actual structure of the system determines the exact relation between the input r(t) and the output c(t) of the system and specify the output for every input.

There are various types of systems such as mechanical system, electrical system, electromechanical system, biological system, etc. All the physical devices such as an electric motor, generator, filter, turbine, etc. are also examples of systems.

Depending upon the number of input and output, the systems may be single input and single output systems or multi input and multi output systems.

Classification of Systems

Depending upon the time domain, the systems may be classified into two categories −

• Continuous-Time Systems
• Discrete-Time Systems

Continuous-Time System

A system which transforms a continuous-time input signal into a continuoustime output signal is called the continuous-time system.

A signal is said to be continuous-time signal if it is defined for every instant of time.

If r(t) and c(t) are the input and output signals of a continuous time system respectively, then the relation between input and output signals of the continuous time system is defined as

𝑐(𝑡) = 𝑇[𝑟(𝑡)]

The block diagram of a continuous-time system is shown in Figure-2.

Amplifiers, integrators, differentiators and filter circuits, etc. are some examples of continuous time systems.

Discrete-Time System

A system which processes the discrete-time input signals and produces discretetime output signals is shown as discrete-time system.

A signal is said to be discrete time signal if it is defined only at the discrete instants of time.

If r(n) and c(n) are the input and output signals of a discrete time system respectively, then the relation between input and output of the discrete-time system is defined as

𝑐(𝑛) = 𝑇[𝑟(𝑛)]

The block diagram of the discrete-time system is represented in Figure-3.

Microprocessors, digital devices, semiconductor memories, shift registers, etc. are some examples of discrete-time systems.