Figure 3.3: Temporal filtering can approximate spatial translation. This effect is demonstrated here on a ID signal, but equally applies to 20. The input signal is shown at two time instants: I(x, t) = f(x) at time t and I(x, t + 1) = f(x + 8) at time t + 1. The first-order Taylor series expansion of I(x, t + 1) about x approximates well the translated signal. The temporal bandpass is amplified and added to the original signal to generate a larger translation. In this example a= 1, magnifying the motion by 100%, and the temporal filter is a finite difference filter, subtracting the two curves.