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== Question == | == Question == |
Revision as of 10:20, 11 November 2011
Contents
Practice Problem on time-invariance of a CT system
Question
Y(t) = x(t − 1) − x(1 − t)
It is Time Invariant? Justify.
Answer
No.
S1 = Y(t) = x(t − 1) − x(1 − t)
S2 = Y(t) = x(t − to)
x(t) − > S1 − > S2 − > x(t − to − 1) − x(1 − t + to)
x(t) − > S2 − > S1 − > x(t − to − 1) − x(1 − t − to)
x(t − to − 1) − x(1 − t + to) = / = x(t − to − 1) − x(1 − t − to)
Comments
Please comment on this answer. Are there any mistakes? Is it clear? Could it be improved?
Comment 1
Actually this is where I'm unsure on HW3 Q1b. It would definitely be improved and more clear if the student showed intermediate steps.
x(t) −> [S1] −> y(t) = x(t - 1) - x(1 - t) --> [S2] −> z1(t) = y(t - to) = x((t - to) -1) - x(1 - (t - to))
--> z1(t) = x(t − to − 1) − x(1 − t + to)
x(t) −> [S2] −> y(t) = x(t - to) --> [S1] −> z2(t) = y(t - 1) - y(1 - t) = x((t - 1) - to) - x((1 - t) - to)
--> z2(t) = x(t − to − 1) − x(1 − t − to)
Comment 2
Write it here