Question

An information signal is of the form s(t) = sin(2*pi*t)/t. The signal amplitude modulates a carrier of frequency 10Hz.

Find and sketch the Waveform and Fourier transform of the transmitted signal before and after AM modulation. For AM modulation you can consider the simple case of DSB format (or double-sideband suppressed carrier modulation).

Answer 1

MATLAB CODE

fs=5000;
t=0:1/fs:5;
fc=10;
xc=cos(2*pi*fc*t); % Carrier wave
f=sin(2*pi*t); % Message Wave
figure(1)
subplot(3,1,1),plot(t,xc); % plotting all signal in Time Domain
title('carrier signal ');
xlabel('time (sec)');
ylabel('amplitude');
subplot(3,1,2),plot(t,f);
title('message signal');
xlabel('time (sec)');
ylabel('amplitude');
% DSB-SC MODULATION
z1= f.*xc;
subplot(3,1,3),plot(t,z1);
title('DSB-SC MODULATION IN TIME DAOMAIN');
xlabel('time (sec)');
ylabel('amplitude');

l1=length(z1);
f=linspace(-fs/2,fs/2,l1); % Frequency Axis
Z=fftshift(fft(z1,l1)/l1); % Fourier transform of DSB-SC
X=fftshift(fft(f,l1)/l1); % Fourier transform of message signal
figure(2)
subplot(2,1,1),plot(f,abs(X));
xlim([-10 10])
title('FOURIER TRANSFORM(SPECTRUM) OF s(t) BEFORE MODULATION ');
xlabel('frequency(hz)');
ylabel('amplitude');
subplot(2,1,2),plot(f,abs(Z)); % plotting Magnitude Spectrum
xlim([-10 10])
title('DSB SC MODULATION IN FREQUENCY DOMAIN');
xlabel('frequency(hz)');
ylabel('amplitude');

RESULTS:

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