Reduce Operator – DownSampling without aliasing:
Usually a 5 or 7 tap separable 1D filter like a (1,4,6,4,1) or a (1,6,15,20,15,6,1) filter is used.
We need half the number of pixels:
An easy example , each odd pixel gets 5 separately filtered by (1,4,6,4,1) filter.
Reproducing / Expanding Operator – UpSampling without aliasing:
Reproducing / Expanding the Odd pixels of the upper level:
Use a 3 tap filter – that is the even pixels (2,4) get a value of zero when upscaled because they are not real, and they are not used (so we only multiply the scale (1,6,1) for the odd pixels.
Reproducing / Expanding the Even Pixels of the upper level: Use a 3 tap filter and use only the odd pixels to scale up by adding them and using half their summed value.
