I need someone to detail the following simulation and what would be the results? PS: I am a novice in using MATLAB and would like to understand.

bit_rate = 5;

f = 5;

fs = 4000;

x = [0 0 0 1 1 0 1 1 1 0 0 0 1];

t = 0:1/fs:1/bit_rate-1/fs;

time = 0:1/fs:(1/bit_rate*length(x))-1/fs;

% Modulation

signal=[];

forn=1:length(x);

if x(n)==1;

y=1.*cos(2*pi*f*t);

else

y=1.*cos(2*pi*f*t + pi);

end

signal=[signal y];

end

% Demodulation

result = []

j = 0;

fori=1:length(x);

a = trapz(signal(j+1:j+length(t)) .* cos(2*pi*f*t));

b = trapz(signal(j+1:j+length(t)) .* cos(2*pi*f*t + pi));

if a > b;

result = [result 1];

else

result = [result 0];

end

j = j+length(t);

end

display(result);

Answer 1

[Sriram Tadavarty]

Hi Jeffy,

Here is the annotated code with explanation. This code basically does phase modulation and demodulation.

bit_rate = 5; % how frequent the bits are transmitted, to calculate the bit duration
f = 5; % Frequency of the signal or the carrier
fs = 4000; % Sample rate
x = [0 0 0 1 1 0 1 1 1 0 0 0 1]; % Input bits
t = 0:1/fs:1/bit_rate-1/fs; % Sampling each bit (it turns out to be time duration of one symbol after sampling)
time = 0:1/fs:(1/bit_rate*length(x))-1/fs; % total duration of the signal
% Modulation
signal=[]; % Initialize the variable to store the output signal
for n=1:length(x) % Loop over each bit to perform the phase modulation
    
if x(n)==1 % If the value of bit is 1, transmit the carrier signal (i.e. cos(*pi*f*t)) without any phase deviation
       y=1.*cos(2*pi*f*t);
    
else % If the value of bit is 0, transmit the carrier signal with a value shifted by pi
        y=1.*cos(2*pi*f*t + pi);
    
end
     signal=[signal y]; % Append the signal for all the bits
end
% Demodulation
result = []; % Initialize a variable to store the result
j = 0; % Loop variable to select the duration of each bit
for i=1:length(x) % Perform demodulation for each bits
    a = trapz(signal(j+1:j+length(t)) .* cos(2*pi*f*t)); % This integratres the signal multiplied with cos(2*pi*f*t) 
    b = trapz(signal(j+1:j+length(t)) .* cos(2*pi*f*t + pi)); % This integratres the signal multiplied with cos(2*pi*f*t+pi)
    
if a > b % Decision threshold
    % If the correlation obtained by integration of the signal multiplied
    % with cos(2*pi*f*t) is greater than the correlation obtained by
    % integration multiplied with cos(2*pi*f*t+pi), Then the decision is
    % the transmitted signal is 1 and append this it to the result
        result = [result 1];
    
else
    % If the correlation obtained by integration of the signal multiplied
    % with cos(2*pi*f*t) is less than  or equal the correlation obtained by
    % integration multiplied with cos(2*pi*f*t+pi), Then the decision is
    % the transmitted signal is 0 and append this it to the result
        result = [result 0];
    
end
    j = j+length(t); % loop over all the bits
end
display(result); % Display the demodulated bits

Hope this helps.

Regards,

Sriram

[jeffyjohnson61]

Yes it does.

Thanks a Lot.

[Sriram Tadavarty]

HI Jeff,

Please do accept the answer, if helped.