4. Shift invariance

Again, we can't talk of shift variance/invariance with these systems as the independent variable for the input and output signals is not the same. But we can examine what happens to the spectrum of a signal on time-shifting it, and vice-versa.

Notice that nowhere has the magnitude of X(f) changed. Only a phase (or argument) change that is linear in frequency has taken place.

Let us, using Duality examine the effect of translating the spectrum on the time-signal.