Consider the sequence of images shown. The image on the left is a segment of an X-ray imag...

Consider the sequence of images shown. The image on the left is a segment of an X-ray image of a commercial printed circuit board. The images following it are, respectively, the results of subjecting the image to 1, 10, and 100 passes of a Gaussian highpass filter with D0 = 30. The images are of size 330 × 334 pixels, with each pixel being represented by 8 bits of gray. The images were scaled for display, but this has no effect on the problem statement.

(a) It appears from the images that changes will cease to take place after some finite number of passes. Show whether or not this in fact is the case. 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.

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(b) If you determined in (a) that changes would cease after a finite number of iterations, determine the minimum value of that number.