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Unformatted text preview: numerically is to zeropad b to 2*L = 14 points, then take every *other* coefficient in the DFT. The MATLAB code is b = [ 1 2 2 1 4 1 2 2 1 ].' B = fft(b,14) H = B(1:2:13) xL = [ 1 1 0 3 1 2 0 ].' XL = fft(xL) YL = H.*XL yL = ifft(YL) bar(0:6,yL) and the resulting yL vector is [20 3 20 10 21 14 12]' Alternatively: b = [ 1 2 2 1 4 1 2 2 1].' B = fft(b,14) xL = [ 1 1 0 3 1 2 0 ].' Sheet1 Page 2 xL2 = [xL XL2 = fft(xL2) YL2 = B.*XL2 yL2 = ifft(YL2) yL = yL2(1:7) Sheet1 Page 3 Sheet1 Page 4 xL] % two periods of xL % oddindexed entries are zero % no need to sample evenindexed entries % two periods of yL...
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 Spring '08
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