(New page: A system is called''' time invariant''' if for any input signal x(t)(x[n]) and for any t0 belongs to R, the response to the shifted inputX(t-t0) is the shifted output y(t-t0). '''Example'...) |
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A system is called''' time invariant''' if for any input signal x(t)(x[n]) and for any t0 belongs to R, the response to the shifted inputX(t-t0) is the shifted output y(t-t0). | A system is called''' time invariant''' if for any input signal x(t)(x[n]) and for any t0 belongs to R, the response to the shifted inputX(t-t0) is the shifted output y(t-t0). | ||
| − | '''Example''': | + | .<pre>'''Example''': |
X(t) ->SYSTEM -> y(t) = 10 x(t) is time invariant because | X(t) ->SYSTEM -> y(t) = 10 x(t) is time invariant because | ||
| − | X(t) -> t0 -> y(t) = X(t-t0) -> SYSTEM -> z(t) = 10 y(t) = 10 x(t-t0) | + | X(t) -> t0 -> y(t) = X(t-t0) -> SYSTEM -> z(t) = 10 y(t) = 10 x(t-t0)</pre> |
where as a system is called '''time variant''' when we find an input signal for which the condition of time invariance is violated. | where as a system is called '''time variant''' when we find an input signal for which the condition of time invariance is violated. | ||
| − | '''Example:''' | + | .<pre>'''Example:''' |
y[n] = nx[n] | y[n] = nx[n] | ||
| − | '''Proof''': consider an input signal x1[n] = d[n] which yields an output y1[n] that is identically 0.However the input x2[n] = d[n-1] yields the output y2[n] = nd[n-1] = d[n-1]. | + | '''Proof''': consider an input signal x1[n] = d[n] which yields an output y1[n] that is identically 0.However the input x2[n] = d[n-1] yields the output y2[n] = nd[n-1] = d[n-1].</pre> |
Latest revision as of 18:21, 9 September 2008
A system is called time invariant if for any input signal x(t)(x[n]) and for any t0 belongs to R, the response to the shifted inputX(t-t0) is the shifted output y(t-t0).
.'''Example''': X(t) ->SYSTEM -> y(t) = 10 x(t) is time invariant because X(t) -> t0 -> y(t) = X(t-t0) -> SYSTEM -> z(t) = 10 y(t) = 10 x(t-t0)
where as a system is called time variant when we find an input signal for which the condition of time invariance is violated.
.'''Example:''' y[n] = nx[n] '''Proof''': consider an input signal x1[n] = d[n] which yields an output y1[n] that is identically 0.However the input x2[n] = d[n-1] yields the output y2[n] = nd[n-1] = d[n-1].
