An analog signal yt sin500pi t pi4 sin1200 pi t is sampled

An analog signal y(t) sin(500pi t + pi/4) + sin(1200 pi t) is sampled at a rate of f_s = 700Hz to produce a discrete-time signal y[n] as the following figure. Write a MATLAB code to perform following tasks: Generate 1400 samples of signal y[n]. Use fft command, compute the 1024-point Discrete Fourier Transform of y[n] and plot the magnitude spectrum of y[n] with frequency axis in Hz. From the magnitude spectrum in (b-iii), determine all the frequency components present in signal y[n] in the frequency region 0 Hz to 700Hz. Explain why these frequencies exist in the spectrum. The signal y[n] is input to a three-sample averaging system to produce the output p[n] = (y[n] + y[n - 1] + y[n - 2])/3. Implement this averaging system and plot the first 100 samples of y[n] and p[n].

Solution

% Verifying the Sampling theorem

t=-10:0.001:10;

% continuous time signal x(t)

fm=0.1;

xt=cos(2*pi*fm*t);

subplot(2,2,1);plot(t,xt);

title(\'continuous time signal x(t)\');

% sampled signal with fs<2fm

fs1=0.1;

n1=-5:5;

x1n=cos(2*pi*fm*n1/fs1);

subplot(2,2,2);stem(n1,x1n);

title(\'sampled signal signal with fs<2fm\');

% sampled signal with fs=2fm

fs2=0.2;

n2=-5:5;

x2n=cos(2*pi*fm*n2/fs2);

subplot(2,2,3);stem(n2,x2n);

title(\'sampled signal signal with fs=2fm\');

% sampled signal with fs>2fm

fs3=0.8;

n3=-10:10;

x3n=cos(2*pi*fm*n3/fs3);

subplot(2,2,4);stem(n3,x3n);

title(\'sampled signal signal with fs>2fm\');

Result:

                  The Sapling theorem for different sampling conditions was verified and plotted.