Given an image of size M × N, you are asked to perform an experiment that consists of repeatedly lowpass filtering the image using a Gaussian lowpass filter with a given cutoff frequency D0. You may ignore computational round-off errors. Let cmin denote the smallest positive number representable in the machine in which the proposed experiment will be conducted.
(a) Let K denote the number of applications of the filter. Can you predict (without doing the experiment) what the result (image) will be for a sufficiently large value of K? If so, what is that result?
(b) Derive an expression for the minimum value of K that will guarantee the result that you predicted.
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