Page 16 - 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

Time invariant system:
A system is said to time invariant if the relationship between the input and output does
not change with time.
If =
Then − = ( − ) should be satisfied for the system to be time invariant
0
0
Time variant system:
A system is said to time variant if the relationship between the input and output changes
with time.
If =
Then − ≠ ( − ) should be satisfied for the system to be time variant
0
0

1.5.5 Causal and Non-Causal system
Continuous time domain:
Causal system:
A system is said to be causal if the response of a system at any instant of time depends
only on the present input, past input and past output but does not depends upon the future
input and future output.
Example: ( ) = 3 ( ) + ( − 1)
A system is said to be causal if impulse response ( ) is zero for negative values of
i.e., ( ) = 0 < 0
Non-Causal system:
A system is said to be Non-causal if the response of a system at any instant of time
depends on the future input and also on the present input, past input, past output.
Example: ( ) = ( + 2) + ( − 1)
( ) = (− ) + ( + 4)
A system is said to be non-causal if impulse response ( ) is non-zero for negative values of
i.e., ( ) ≠ 0 < 0

Discrete time domain:
Causal system:
A system is said to be causal if the response of a system at any instant of time depends
only on the present input, past input and past output but does not depends upon the future
input.
Example: ( ) = 3 ( ) + ( − 1)
A system is said to be causal if impulse response h(n) is zero for negative values of n
i.e., ( ) = 0 < 0

Non-Causal system:
A system is said to be Non-causal if the response of a system at any instant of time
depends on the future input and also on the present input, past input, past output.
Example: ( ) = ( + 2) + ( − 1)

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