Question

- Generate a Matlab Code for amplitude modulated signal by multiplying a message signal (a low frequency cosine signal) with a carrier signal (a high frequency cosine signal).

- Sketch the Fourier transform of the modulated signal.

- Demodulate the modulated signal (with no noise) by again multiplying it with the same carrier signal.

- Sketch the Fourier transform of the signal obtained in c).

- Your task is to recover the message signal from the signal in c). Determine the type of filter you have to use and get its coefficients.

- Apply filter coefficients to the signal in c) and check whether the filtered signal is similar to the original message signal in time domain?

- Repeat the above steps from c) by adding zero-mean Gaussian distributed noise to the modulated signal. Check if the same filter works using small, medium, and large values of noise power. Comment on your results.

Answer #1

**Script:**

clc;clear all;close all;

%Message signal

fs=40000

t=0:1/fs:0.01;

fm=1000;

Am=sin(2*pi*fm*t);%low frequency cosine signal

fc=10000;

Ac=cos(2*pi*fc*t);%high frequency cosine signal

%Amplitude modulation

N=1024;f=[-fs/2:fs/N:fs/2-fs/N];

xAM=Am.*Ac;

f=[-fs/2:fs/N:fs/2-fs/N];

%Frequency domain of AM

figure;

subplot(311)

plot(f,fftshift(abs(fft(Am,N))),'b') ;

title('Fourier transform of Modulated signal');

xlabel('f in Hz');ylabel('XAM(f)');grid on;

xlim([-5000,5000])

%Demodulation

demod = xAM.*cos(2*pi*fc*t);

subplot(312)

plot(f,fftshift(abs(fft(demod,N))),'m') ;

title('Fourier transform of demodulated signal');

xlabel('f in Hz');ylabel('XDEMOD(f)');grid on;

xlim([-5000,5000])

%Filter design to recover message signal

[num den] = butter(5,fc*2/fs);

mf = filtfilt(num,den,demod).*2;

subplot(313)

plot(t,mf,'r','LineWidth',3,t,Am,'--b','LineWidth',3);grid
on;

title('Demodulation ')

xlabel('t(s)')

legend('demodulated signal','Original message signal')

Specify the frequency response characteristics of a VSB filter
that passes the lower sideband and the first frequency component of
the upper sideband of a DSB modulated signal with the message
signal given by m(t)=10cos(3000(pi)t)+20cos(6000(pi)t) . The
carrier signal has an amplitude of 20 and a frequency of 250
kHz.
a. Write the expression for the DSB signal.
b. Write the expression for the single sided spectrum of the DSB
signal
c. Sketch the spectrum
d. Give the specifications for...

Below are three different codes in Matlab, please copy those
your matlab and answer the following questions:
Thank you for your help!!!!
1.1 Baseband Signal
a) Plot time versus baseband signal (m_sig).
b) Plot freq versus baseband signal spectrum (M_fre).
1.2 Amplitude Modulation – Suppressed Carrier.
a) Plot time versus the DSB-SC signal (s_dsb).
b) Plot freq versus the DSB-SC signal spectrum (S_dsb).
1.3 Coherent Demodulation
a) Plot freq versus the pre-filtered signal (S_dem).
b) Plot freq versus the post-filtered...

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