Question

Using the course Matlab dtft function compute the magnitude, and phase for the following discrete-time signal а) x(п) -п(09)[«(п)-и (п-21)] F [(a) -и (п- 40)] b) x (п) - =coS n 10 4 u --

Answer 1

The first signal exists for n=0 to n=20 after which it is zero and the second signal exists for n=0 to n=39. The following are the MATLAB codes and the corresponding plots.

Part a.

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n=0:1:20;
x=n.*(0.9).^(n);
w=-pi:.01:pi;
for i=1:length(w)
X(i)=sum(x.*exp(-1i*w(i)*n));
end
subplot(1,2,1);plot(w,abs(X));title('Magnitude plot');xlabel('\omega');ylabel('Magnitude');
subplot(1,2,2);plot(w,angle(X));title('Phase plot');xlabel('\omega');ylabel('Phase (radians)');

Part b.

Phase plot Magnitude plot 50 50 40 30P 20 10 apnyuew Phase (radians)

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n=0:1:39;
x=cos((n*pi)/10-pi/4);
w=-pi:.01:pi;
for i=1:length(w)
X(i)=sum(x.*exp(-1i*w(i)*n));
end
subplot(1,2,1);plot(w,abs(X));title('Magnitude plot');xlabel('\omega');ylabel('Magnitude');
subplot(1,2,2);plot(w,angle(X));title('Phase plot');xlabel('\omega');ylabel('Phase (radians)');

Phase plot Magnitude plot 4 25 3 20 2 15 10 2 5 -3 -4 -4 0 -4 4 2 -2 A 7 N + N Phase (radians) - LO Magnitude