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x(t) -> [sys] -> y(t) = x*(t-1) | x(t) -> [sys] -> y(t) = x*(t-1) | ||
| − | x(t) -> [sys] -> y(t) = x*(t-1) -> [Time Delay] = z(t) = y*(t-1) = [y*(t-1-to)] | + | |
| + | x(t) -> [sys] -> y(t) = x*(t-1) -> [Time Delay]-> = z(t) = y*(t-1) = [y*(t-1-to)] | ||
| + | |||
These two outputs are not the same. According to this change, the time does get varied based on the shift in the subscript. This proves that the system is Time-Variant. | These two outputs are not the same. According to this change, the time does get varied based on the shift in the subscript. This proves that the system is Time-Variant. | ||
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x(t) -> [sys] -> y(t) = 2*x^2(t) | x(t) -> [sys] -> y(t) = 2*x^2(t) | ||
| − | x(t) -> [sys] -> y(t) = 2*x^2(t) -> [Time Delay] = z(t) = y*(t-to) = 2*x^2(t-to) | + | |
| + | x(t) -> [sys] -> y(t) = 2*x^2(t) -> [Time Delay]-> = z(t) = y*(t-to) = 2*x^2(t-to) | ||
| + | |||
| + | |||
These outputs are the same which thus shows that the system is in fact Time Invariant. | These outputs are the same which thus shows that the system is in fact Time Invariant. | ||
Latest revision as of 12:22, 12 September 2008
Time Invariance
If a system is time invariant then its input signal x(t) can be shifted by (t-to) and its output will be the same signal, yet it will be shifted the same throughout the system.
Ex: Time Variant
x(t) -> [sys] -> y(t) = x*(t-1)
x(t) -> [sys] -> y(t) = x*(t-1) -> [Time Delay]-> = z(t) = y*(t-1) = [y*(t-1-to)]
These two outputs are not the same. According to this change, the time does get varied based on the shift in the subscript. This proves that the system is Time-Variant.
Ex: Time Invariant
x(t) -> [sys] -> y(t) = 2*x^2(t)
x(t) -> [sys] -> y(t) = 2*x^2(t) -> [Time Delay]-> = z(t) = y*(t-to) = 2*x^2(t-to)
These outputs are the same which thus shows that the system is in fact Time Invariant.
