Page 14 - EC8352 -SS-NOTES-by Prof.Bokhari ECE/MAMCET

SUBJECT: EC8352- Signals and Systems
AUTHOR: M.SHAKUNTHALA, A.P/ECE/RMDEC
Dr.M.N.VIMAL KUMAR, AP/ECE/RMDEC

Response =
where ( ) is input signal, ( ) is output signal, and T denotes transformation

( ) T ( )

Fig 1.84 Representation of continuous time system
Discrete time system:
Discrete time system operates on a discrete time signal (input or excitation) and
produces another discrete time signal (output or response) which is shown in Fig 1.85.

The signal ( ) is transformed by the system into signal ( ), this transformation can be
expressed as,
Response =
where x(n) is input signal, y(n) is output signal, and T denotes transformation
( ) T ( )

Fig 1.85 Representation of discrete time system

1.5.2 Linear system and Non Linear system
Continuous time domain:
Linear system:
A system is said to be linear if it obeys superposition theorem. Superposition theorem
states that the response of a system to a weighted sum of the signals is equal to the
corresponding weighted sum of responses to each of the individual input signals.
Condition for Linearity:
+ = + ( )
2
1
2
1

2
2
1
1
Non Linear system:
A system is said to be Non linear if it does not obeys superposition theorem.
. . , + ≠ + ( )
2
2
1
1
where y t and y t are the responses of x t and x t respectively
1
2
2
1

Discrete time domain:
Linear system:
A system is said to be linear if it obeys superposition theorem. Superposition theorem
states that the response of a system to a weighted sum of the signals is equal to the
corresponding weighted sum of responses to each of the individual input signals.
Condition for Linearity:
+ = + ( )
2
2
1
1
where y n and y n are the responses of x n and x n respectively
2
1
2
1
Non Linear system:
A system is said to be Non linear if it does not obeys superposition theorem.
. . , + ≠ + ( )
2
1
1
2

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