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).

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'''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.

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'''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].

Alumni Liaison

Prof. Math. Ohio State and Associate Dean
Outstanding Alumnus Purdue Math 2008

Jeff McNeal