Question

Using the MATLAB M-file dft, compute the 32-point DFT of rn cos(₩), 0 〈 n < 10, x[n] 0 for all other n. COS

M-file

dft.m

function Xk = dft(x)
[N,M] = size(x);
if M ~=1, % makes sure that x is a column vector
x = x';
N = M;
end
Xk=zeros(N,1);
n = 0:N-1;
for k=0:N-1
Xk(k+1) = exp(-j*2*pi*k*n/N)*x;
end

Answer 1

function Xk = dft(x,N)
M=length(x);
if M>N
disp('N must be >=M')
end
xnew=[x (zeros(1,N-M))]
for k=0:1:N-1  
for n=0:1:N-1
xk(k+1,n+1)=exp(-j*2*pi*k*n/N);
end
end
Xk=xk*xnew'

Program:

N=32
n=0:1:10
xn=cos(10*n*pi/11)
Xk=dft(xn,N)
%__________________________________
%plots
k=0:1:N-1;
subplot(311)
stem(n,xn,'k')
title('Sequence in time domain x(n)')
xlabel('n')
ylabel('x(n)')
subplot(312)
stem(k,abs(Xk),'r')
title('DFT of x(n)-Magnitude response')
xlabel('k')
ylabel('|X(k)|')
subplot(313)
stem(k,angle(Xk),'m')
title('DFT of x(n)-Phase response')
xlabel('k')
ylabel('<X(k)')