This is particularly true when filtering a space axis. An advantage of the folding is that a constant-valued signal is unchanged by the smoothing. This is desirable since a smoothing filter is a low-pass filter which naturally should pass the lowest frequency without distortion. The result is like a wave reflected by a zero-slope end condition. Impulses are smoothed into triangles except near the boundaries.
Inputs are spikes at various distances from the edge.
Note that at the boundary, there is necessarily only half a triangle, but it is twice as tall. For example, the output can share the same location as the input. This is a discrete representation of a rectangle function. Identify the ways in which it is similar to and different from the sinc function. Explain the signal second from the bottom in Figure 3 .