You know from Table 4.2 that the dc term, F(0, 0), of a DFT is proportional to the average...

You know from Table 4.2 that the dc term, F(0, 0), of a DFT is proportional to the average value of its corresponding spatial image. Assume that the image is of size M × N. Suppose that you pad the image with zeros to size P × Q, where P and Q are given in Eqs. (4.6-31) and (4.6-32). Let Fp(0, 0) denote the dc term of the DFT of the padded function.

(a) What is the ratio of the average values of the original and padded images?

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(b) Is Fp(0, 0) = F(0, 0)? Support your answer mathematically.

TABLE 4.2

Summary of DFT definitions and corresponding expressions.

(4.6-31)

(4.6-32)