The problem given in my textbook is:
y(t) = x(t-5) - x(3-t)
Show that this system is time-invariant.
Um, isn't this system time varying?
The second term involved a time inversion, doesn't this make it time varying?
e.g. g(3-t) = g(-(t-3))
That is:
Let x1(t) = g(t), Then y1(t) = g(t-5) - g(3-t)
Let x2(t) = g(t-t0), Then y2(t) = g(t-t0-5) - g(3-t-t0)
y1(t-t0) = g((t-t0)-5) - g(3-(t-t0)) = g(t-t0-5) - g(3-t+t0) ≠ y2(t)
Thus the system is time-varying.
Am I wrong or is the book?
Thanks
y(t) = x(t-5) - x(3-t)
Show that this system is time-invariant.
Um, isn't this system time varying?
The second term involved a time inversion, doesn't this make it time varying?
e.g. g(3-t) = g(-(t-3))
That is:
Let x1(t) = g(t), Then y1(t) = g(t-5) - g(3-t)
Let x2(t) = g(t-t0), Then y2(t) = g(t-t0-5) - g(3-t-t0)
y1(t-t0) = g((t-t0)-5) - g(3-(t-t0)) = g(t-t0-5) - g(3-t+t0) ≠ y2(t)
Thus the system is time-varying.
Am I wrong or is the book?
Thanks