solvedB34 - numerically is to zero-pad b to 2*L = 14...

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Sheet1 Page 1 S 34.1 (P 4.3) ______________ Divide by 2*pi to express the three frequencies in cycles per sample: 3/28, 9/35 and 17/48 Since these are rational (i.e., integer fractions), the signal is periodic. The period is the smallest integer L such that each frequency can be expressed as k/L. With irreducible fractions (as above), this is given by the least common multiple (LCM) of the denominators: LCM(28,35,48) = 1680 S 34.2 (P 4.7) ______________ The output y is also periodic with period L=7. If xL = x[0:6]and yL = y[0:6] then the DFT's of xL and yL are related by YL[k] = H(exp(j*2*pi*k/8))*XL[k] for k=0:7. The easiest way to obtain the values H(exp(j*2*pi*k/8))
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Unformatted text preview: numerically is to zero-pad 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 % odd-indexed entries are zero % no need to sample even-indexed entries % two periods of yL...
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solvedB34 - numerically is to zero-pad b to 2*L = 14...

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