8/16/2019 315class 40 Matlab Code

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MatLab illustrations for Discrete Fourier Transform (or FFT)

q=5;

omega=0:.01:2*pi;

Xomega=abs(sin((q+.5)*omega))./abs(sin(omega/2));

subplot(2,1,1); plot(omega,Xomega)

x=ones(1,11)'

n=[0:10]'

Omega1=n*omega;

Xomega1=x'*exp(-j*Omega1);

subplot(2,1,2); plot(omega,abs(Xomega1))

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8/16/2019 315class 40 Matlab Code

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q=5;N=88;

x=[ones(1,2*q+1) zeros(1,N-2*q-1)];

Xk=dft(x);

k=0:N-1;

figure(2)

stem(k,abs(Xk))

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8/16/2019 315class 40 Matlab Code

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hold on

plot(k*2*pi/N,abs(Xk),’r’))

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8/16/2019 315class 40 Matlab Code

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Xkshifted=fftshift(Xk);

figure(3)

plot(-pi:2*pi/N:87*2*pi/N,abs(Xkshifted))

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x1=idft(Xk);

stem(0:15,x1(1:16))

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