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Unformatted text preview: (ii) The synthesis equation for a realvalued Npoint vector can be also written as x[n] = X[0]/N + (X[N/2]/N)*(1)^n + sum (2*X[k]/N)*cos(2*pi*k*n/N + angle(X[k])) where the last sum is over 0<k<N/2. Comparing this to the given equation for x[n], we have: X[k] = [0 28 8 0 24 0 8 28].' angle(X[k]) = [ 0 1.2 0.8 0 0 0 0.8 1.2].' (The angle of X[4] equals 0 because X[4]>0; it would have been equal to pi otherwise.) S 13.1 (P 3.10) _______________ x = [ 2 1 1 2 3 3 ].' We have: x1 = P*x = [3 2 1 1 2 3].' x2 = (P^5)*x = [1 1 2 3 3 2].' x3 = P*x + (P^5)*x = [4 1 1 4 1 1].' R*x = [2 3 3 2 1 1].' x4 = x + R*x = [4 4 4 4 4 4 ].' x5 = x  R*x = [0 2 2 0 2 2].' F^3 = diag([1 1 1 1 1 1]), so x6 = (F^3)*x = [2 1 1 2 3 3].' x7 = x  (F^3)*x = [0 2 0 4 0 6].'...
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 Spring '08
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