Question

This question should be solved by MATLAB.

- Generate an analog signal. (This should be an audio, any audio can be used.)

- Analyze frequency spectrum of this analog signal.

- Modulate it. (AM Modulation can be used)

- Send the modulated signal over a wireless channel. (Before sending the signal, a noise should be added.)

Thank you already for your help!

Answer 1

Solution:

(a)the analog audio signal contains three frequency components 1KHz,5KHz,8KHz

%%--------------------- MATLAB code -------------------------%%

dt=1/100;
dt=1/10000; %sampling rate
et=4e-2; %end of the interval
t=0:dt:et; %sampling range
%frequencies
f1=1e3;f2=2e3;f3=3e3;
y=5*sin(2*pi*f1*t)+2*sin(2*pi*f2*t)+6*sin(2*pi*f3*t); % sample the signal
%plot the time domain
subplot(2,1,1); %first of two plot
plot(t,y,'r');grid on; %plot with grid
axis([0 et -10 10]); %adjust scaling
xlabel('time') %time axis
ylabel('amplitude') %freqency axis
title('Time Domain')

%%(b)
%Analysis in Frequency spectrum
Y=fft(y); %compute the fourier transform
n=size(y,2)/2; %second half are complex conjugate
amp_spectrum=abs(Y)/n; %absolute value and normalize
subplot(2,1,2); %second of two plots
freq=(0:79)/(2*n*dt); % abscissa viewing window
plot(freq,amp_spectrum(1:80)); %plot amplitude spectrum
grid on;
xlabel('freqency') %x label frequency
ylabel('amplitude Spectrum') %y axis amplitude spectrum
title('Freqency Domain')

%%-------------------------- END --------------------------%%

plot:

Time Domain 10 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 time Freqency Domain 4 0 200 400 600 800 1000 1200 1400 1600 1800 2000 freqency

(c)modulating the message signal

%%--------------------------- MATLAB Code ---------------------------%%

Ac=input('enter carrier signal amplitude:');
%Am=input('enter message signal amplitude');
fc=input('enter carrier frequency more then 6k:');
%fm=input('enter message frequency');% fm<fc
m=input('enter modulation index:');
T=input('enter time period:');
dt=1/100;
dt=1/10000; %sampling rate
et=T*1e-2; %end of the interval
t=0:dt:et; %sampling range
%t1=linspace(0,t,1000);
%y1=sin(2*pi*fm*t1); % message signal
%frequencies
f1=1e3;f2=2e3;f3=3e3;
y1=5*sin(2*pi*f1*t)+2*sin(2*pi*f2*t)+6*sin(2*pi*f3*t); % sample the signal
y2=sin(2*pi*fc*t); % carrier signal
eq=(1+m.*y1).*(Ac.*y2);
subplot(311);
plot(t,y1);
xlabel('Time');
ylabel('Amplitude');
title('Message signal')
subplot(312)
plot(t,y2);
xlabel('Time');
ylabel('Amplitude');
title('Carrier signal');
subplot(313);
%plot(t,eq);
plot(t,eq,'r');
xlabel('Time');
ylabel('Amplitude');
title('Modulated signal');

%%----------------------------------- END -------------------------------%%

plot:

Message signal 20 20 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Time Carrier signal 0 0.01 .02 0.03 0.04 0.05 0.06 0.07 0.08 Time Modulated signal 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Time