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Symmetry in DFT plot in MATLAB

%Code for DFT of a simple sine signal:

clc
clear all
close all
N=16;
n=0:N-1;
w=2*pi/N;
x=sin(w*n);
y=fft(x,N);
k=n;
subplot(2,1,1);
stem(k,abs(y));
subplot(2,1,2);
stem(k,angle(y));





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MATLAB