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DFT Sinusoids for $ N=8$

Below is the Matlab for Fig. 6.2:

N=8;
fs=1;

n = [0:N-1]; % row
t = [0:0.01:N]; % interpolated
k=fliplr(n)' - N/2;
fk = k*fs/N;
wk = 2*pi*fk;
clf;
for i=1:N
    subplot(N,2,2*i-1);
    plot(t,cos(wk(i)*t))
    axis([0,8,-1,1]);
    hold on;
    plot(n,cos(wk(i)*n),'*')
    if i==1
	title('Real Part');
    end;
    ylabel(sprintf('k=%d',k(i)));
    if i==N
	xlabel('Time (samples)');
    end;
    subplot(N,2,2*i);
    plot(t,sin(wk(i)*t))
    axis([0,8,-1,1]);
    hold on;
    plot(n,sin(wk(i)*n),'*')
    ylabel(sprintf('k=%d',k(i)));
    if i==1
	title('Imaginary Part');
    end;
    if i==N
	xlabel('Time (samples)');
    end;
end


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``Mathematics of the Discrete Fourier Transform (DFT)'', by Julius O. Smith III, W3K Publishing, 2003, ISBN 0-9745607-0-7.

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Copyright © 2003-10-09 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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