Compute the eight-point circular convolution for the following sequences

(a) x1(n) = {1, 1, 1, 1, 0, 0 ,0 ,0}

x2(n) = sin 3?/8n 0 ? n ? 7

(b) x1(n) = (1/4)n 0 ? n ? 7

x2(n) = cos 3?/8n 0 ? n ? 7

(c) Compute the DFT of the two circular convolution sequences using the DFTs of x1(n) and x2(n).

Central to the operation of a photocopy machine (see Section 16.2) is a drum coated with a photoconductor-a semiconductor that is a good insulator in the dark but allows charge to flow freely when illuminated with light. How does light allow charge to flow freely through the semiconducting material? How large should the band gap be for a good photoconductor? If the drum gets hot, is the contrast between light and dark areas on the image improved or degraded?

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