Adding the Outputs of two FIR Filters

The left column shows the image processed by a high-pass filter, while the right column uses a low-pass filter. When the two images are added together, we get the original image back, because all the frequency content has been included. This experiment confirms the linearity (additivity) of the spectrum.
HIGH-PASS FILTER CHANNEL LOW-PASS FILTER CHANNEL
h45htiny.png Filter with different filters h45ltiny.png
v_add.gif Rather different results w_add.gif
Add the two together and ....
y.gif
... we are back where we started!
y.gif