*y(t) = x(t-5) - x(3-t)*

Show that this system is time-invariant.

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