CCS

Demodulation of PAM Signals

 

 

Matlab Coding

 1 % MATLAB script
echo on
T=1;
delta_T=T/200;                     % sampling interval
alpha=0.5;                         % rolloff factor
fc=40/T;                           % carrier frequency
A_m=1;                             % amplitude
t=-5*T+delta_T:delta_T:5*T;        % time axis
N=length(t);
for i=1:N,
    if (abs(t(i))~=T/(2*alpha)),
        g_T(i) = sinc(t(i)/T)*(cos(pi*alpha*t(i)/T)/(1-4*alpha^2*t(i)^2/T^2));
    else
        g_T(i) = 0;                 % The value of g_T is 0 at t=T/(2*alpha) and at t=-T/(2*alpha)
    end;                           
    echo off ;
end;
echo on;

G_T=abs(fft(g_T));                   % spectrum of g_T
u_m=A_m*g_T.*cos(2*pi*fc*t);         % the modulated signal
U_m=abs(fft(u_m));                   % spectrum of the modulated signal

% actual frequency scale
f=-0.5/delta_T:1/(delta_T*(N-1)):0.5/delta_T;

% Plotting commands follow.
figure(1);
plot(f,fftshift(G_T));
axis([-1/T 1/T 0 max(G_T)]);
figure(2);
plot(f,fftshift(U_m));

Simulaiton Result

Spectra of baseband signal 

 spectra of amplitude-modulated(bandpass) signal

 

 

 

% MATLAB script

Am = 1;                                 % Signal Amplitude
T = 1;
Ts = 100/T;
fc = 30/T;
t = 0:T/100:T;
l_t = length(t);
g_T = sqrt(2/T)*ones(1,l_t);
si = g_T .* cos(2*pi*fc*t);
var = [ 0 0.05 0.5];                    % Noise variance vector
for k = 1 : length(var)
    % Generation of the noise components:
    n_c = sqrt(var(k))*randn(1,l_t);
    n_s = sqrt(var(k))*randn(1,l_t);
    noise = n_c.*cos(2*pi*fc*t) - n_s.*sin(2*pi*fc*t);
    r = Am*g_T.*cos(2*pi*fc*t)+noise;   % The received signal    
    y = zeros(1,l_t);
    for i = 1:l_t
        y(i) = sum(r(1:i).*si(1:i));    % The correlator output
    end
    % Plotting the results:
    subplot(3,1,k)
    plot([0 1:length(y)-1],y)
    title(['sigma^2 = ',num2str(var(k))])
    xlabel('n')
    ylabel('y(nT_s)')
end

Simulation Result

Reference,

　　1. <<Contemporary Communication System using MATLAB>> - John G. Proakis