Question

Given,

x[n] 2cos ((/5)n)3sin((n/10)n)

(i) In MATLAB, analyze the signal by performing Fourier Transform for -pi <= 0 <= pi. ("<=" represent less than or equal to)

(ii) Comment on your observation.

Answer 1

I have written a code for calculation of fourier transform and printed signal vs time, magnitude of fourier transformed signal vs frequency and phase angle of fourier transformed signal vs frequency

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t=-pi:0.1:pi;
x = 2*cos((pi/5)*t)+ 3*sin((pi/10)*t);
N = length(x);
X = zeros(N,1);
for k = 0:N-1
for n = 0:N-1
X(k+1) = X(k+1) + x(n+1)*exp(-j*pi/2*n*k);
end
end

subplot(311)
stem(t,x);
xlabel('Time (in seconds)');
ylabel('Amplitude');
title('Time vs Input')

subplot(312)
stem(t,X);
xlabel('Frequency');
ylabel('Magnitude');
title('Frequency - Magnitude')

subplot(313)
stem(t,angle(X));
xlabel('Frequency');
ylabel('Phase angle');
title('Frequency - Phase')

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Time vs Input 111すますます Time (in seconds) Frequency Magnitude 60 40 20 20 Frequency Frequency Phase Frequency