Use the FFT and inverse FFT to compute the convolution of a 1, 2, 3, 4 and b 4, 3, 2, 1 , using arithmetic in Z 17 Use the fact that 5 is a generator for the positive elements of Z 17 , and show the output of each component as in Figure 25 1 Figure 25 1 bo,b,b2 b n 1 n 1 Pad with n 0's Pad with n 0's a,a,,az, ,a0,0, ,0 bo,b,,b, ,b,,0,0, ,0 n 1 DFT DFT Component Multiply inverse DFT (Convolution)

Question: Use the FFT and inverse FFT to compute the convolution of a = [1, 2, 3, 4] and b = [4, 3, 2, 1], using

Use the FFT and inverse FFT to compute the convolution of a = [1, 2, 3, 4] and b = [4, 3, 2, 1], using arithmetic in Z₁₇. Use the fact that 5 is a generator for the positive elements of Z₁₇, and show the output of each component as in Figure 25.1.

Figure 25.1.

[bo,b,b2...b] n-1 n-1 Pad with n 0's Pad with n 0's [a,a,,az,.,a0,0,..,0] [bo,b,,b,.,b,,0,0,..,0] n-1 DFT DFT Component Multiply inverse DFT (Convolution)

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