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To check if a system is time-invariant, we can shift the function by a given value of T. Then, we send the | To check if a system is time-invariant, we can shift the function by a given value of T. Then, we send the | ||
function through the system and obtain an output. Now, take the same input function and put it into the system | function through the system and obtain an output. Now, take the same input function and put it into the system | ||
| − | without shifting it first. Then take the output of the system and shift it the value of T used previously. If | + | without shifting it first. Then take the output of the system and shift it by the value of T used previously. If |
these two processes yield the same results, then the system is called "time invariant." | these two processes yield the same results, then the system is called "time invariant." | ||
Revision as of 15:29, 11 September 2008
TIME INVARIANCE
DEFINITION
A system is defined as "time-invariant" when its output is not explicitly dependent on time (t). In other words, if one were to shift the input/output along the time axis, it would not effect the general form of the function.
METHOD
To check if a system is time-invariant, we can shift the function by a given value of T. Then, we send the function through the system and obtain an output. Now, take the same input function and put it into the system without shifting it first. Then take the output of the system and shift it by the value of T used previously. If these two processes yield the same results, then the system is called "time invariant."
SYSTEMS
A.) h1(t) = 2x1(3t) + 5
B.) h2(t) = 6t*x2(3t) + 5
