(→Example of a tume-invariant system) |
(→Example of a tume-invariant system) |
||
| Line 4: | Line 4: | ||
== Example of a tume-invariant system == | == Example of a tume-invariant system == | ||
x(t) = <math>e^t</math> | x(t) = <math>e^t</math> | ||
| + | Output signal y(t) can be <math>10e^t</math> by system | ||
| + | Prove. | ||
| + | 1. <math>e^t -> e^{t-t0}</math> by time delay. | ||
| + | <math>e^{t-t0} -> 10e^(t-t0)</math> by system. | ||
| + | |||
| + | 2. <math>e^t -> 10e^t </math> by system. | ||
| + | <math>10e^t -> 10e^{t-t0}</math> | ||
| + | |||
| + | The output signals are same. Then we can say that the system is time-invariant. | ||
Revision as of 13:54, 9 September 2008
A time-invariant system
For any input signal x(t), a system yelids y(t). Now, suppose input signal shifted t0, x(t-t0). Then output signal also shifted t0, y(t-t0). Then we can say a system is time-invariant.
Example of a tume-invariant system
x(t) = $ e^t $ Output signal y(t) can be $ 10e^t $ by system Prove. 1. $ e^t -> e^{t-t0} $ by time delay.
$ e^{t-t0} -> 10e^(t-t0) $ by system.
2. $ e^t -> 10e^t $ by system.
$ 10e^t -> 10e^{t-t0} $
The output signals are same. Then we can say that the system is time-invariant.
