3015_Homework_5_Solutions

3015_Homework_5_Solutions - (b T=2/3 0 = 3 Xk = 3 2 T 2 t...

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(b) T=2/3, ω 0 = 3π, X k = 3 2 2 ∗ δ t + δ t 1 3 e jk ω 0 t T dt = 3 2 2 + e jk π = 3 + 3 2 e jk π
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k = -5:5; xk= zeros(1, 11); xk(-3+6)=1; xk(-1+6)=-j; xk(1+6)=j; xk(3+6)=1; stem(k,xk) subplot(3,1,1); stem(k,abs(xk)) xlabel('k'); ylabel('abs(X(k))'); title('3.51(a)'); subplot(3,1,2); stem(k,angle(xk)) xlabel('k'); ylabel('angle(X(k))'); t = -2:0.01:2; subplot(3,1,3); plot(t, -2*sin(2*pi*t) + 2*cos(6*pi*t)); xlabel('t'); ylabel('x(t)'); k = -10:10; xk = power(-1/3,abs(k)); subplot(2,1,1); stem(k,xk)
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