Practice Question on "Signals and Systems"


More Practice Problems


Topic: System Properties


Question

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(tto)

x(t) − > S1 − > S2 − > x(tto − 1) − x(1 − t + to)

x(t) − > S2 − > S1 − > x(tto − 1) − x(1 − tto)

x(tto − 1) − x(1 − t + to) = / = x(tto − 1) − x(1 − tto)


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


Back to ECE301 Spring 2011 Prof. Boutin

Alumni Liaison

Recent Math PhD now doing a post-doctorate at UC Riverside.

Kuei-Nuan Lin