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## 9.2. Solved exercises

EXERCISE 9.1.

A digital signal containing 20 binary elements is transmitted on a communication channel. This signal has the following characteristics:

• – binary rate: 1000 symbols/s,
• – sampling frequency: 10 kHz,
• – symbol duration: 1 ms,

1. Using the function subplot plot the signal, the matched filter impulse response and its output signal. Define the decision threshold and the optimal decision moments.

```Rb = 1000; % binary rate
fs = 10000; % sampling frequency
Ts = 1/fs;  % sampling period
Tb = 1/Rb;  % binary element duration
sequence=[0 1 1 1 0 1 0 0 1 0 1 1 1 0 1 0 0 1 0 1];
no= length(sequence);  % number of bits
no_ech = no * Tb/Ts;   % number of samples
t = [0:(no_ech-1)]*Ts; % sampling moments
x=(sequence'*pulse)';  % signal generation
x=x (:);
t_time = Ts * [0:no_ech];
figure
subplot(311);
plot(t_time,[x;0] );
axis([0 0.021 0 1.2]);grid
title('Bandbase signal')
g = (pulse);
h = g(length(g):-1:1); % matched filter impulse response
subplot(312);
plot([0:size(h,2)+1]*Ts,[h 1 0]);
axis([0 0.021 0 1.2]),grid
title('Matched filter impulse response')
y_fil = conv(h,x) ;    % matched filter output signal
y_fil = [y_fil( :)' 0];
subplot(313);
plot([0:size(y_fil,2)]*Ts, [0 y_fil]) ;
axis([0 0.021 0 1.2*max(y_fil)]);grid
xlabel('Time [s]');
title('Matched filter output signal')```

Figure 9.1. Input signal, matched filter impulse response and its output signal ...

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