Systems

SYSTEMS

System is an interconnection of functional blocks. System produces output with respect to an input signal.

Classification of systems

Systems are classified into two types. Thy are continuous time system(CTS) and discrete time (DT) system.

Continuous time system:

Continuous time system operates on continuous time signals.

Example: Amplifiers, analog transmitter and receiver.

Discrete time system:

Discrete time system operates on discrete time signals.

Example: computer, Microprocessor and printer.

Classification of continuous time and discrete time system:

Continuous time system and discrete time system are classified as follows:

1) Static and dynamic system

2) Linear and non linear system

3) Time variant and time invariant system

4) Causal and non causal system

5) Stable and unstable system

1.5.1 Static and Dynamic System

Static system: (Memory less system)

A continuous time system (or) a discrete time system is said to be static if its output depends upon present input only. It does not require memory to store past (or) future input.

Example:

(i) y(t) = sin x(t)

Output y(t) depends upon present input x(t)

(ii) y(n) = x(n) cos(ω₀n)

Output y(n) depends upon present input x(n).

Dynamic system: (System with memory)

A continuous time system (or) a discrete time system is said to be dynamic system if its output depends upon past values of input also.

Example:

Time Variant and Time Invariant System

A continuous time system (or) a discrete time system is said to be time invariant if time shift in the input produces corresponding time shift in the output.

Condition for time invariant system.

CT System :

DT System:

Input x(n) is delayed by k samples. Then output y(n) is also delayed by k samples.

Time variant system:-

A continuous time system (or) a discrete time system is said to be time variant if time shift in the input does not produces corresponding time shift in the output.

Condition for time variant system

Linear and Non Linear Systems.

Linear system:-

A system is said to be linear if it satisfies the superposition principle. Let us consider the two continuous time system. First system with input x₁(t) and output y₁(t). Second system with input x₂(t) and output y₂(t).

Then the continuous time system is linear if

Condition for discrete time system to be linear:

Consider two discrete time system.

First system with input x₁(n) and output y₁(n) and second system with input x₂(n) and output y₂(n).

Then the discrete time system is linear if

Here a₁ and a₂ are arbitrary constants.

Non linear system:-

A system is said to be non linear system if it does not satisfy the superposition principle.

Condition for non linear system:

Causal and Non Causal Systemen

A continuous time system (or) a discrete time system is said to be causal if the output of the system at any time depends upon present and past inputs.

Example:

Continuous time system:- y(t) = e ^{t x(t)}

Here output y(t) depends upon the present input x(t).

Discrete time system: y(n) = |x(n)|

Here output y(n) depends upon the present input x(n).

Non causal system:-

A continuous time system (or) a discrete time system is said to be non causal system if its output depends upon future input also.

Stable and Unstable System

Stable system:

A continuous time system (or) a discrete time system is said to be stable if every bounded input produces bounded output.

The input is said to be bounded if there exists some finite number Kx.

The output is said to be bounded if there exists some finite number Kx.

Unstable system:-

If a continuous time system (or) DT system produces unbounded output for bounded input then the system is said to be unstable system.