Hi Abdelrhman,
As I can see, you have a modulator at the transmitter side, and you want a demodulator at the receiver side to reproduce the original signal.
For this, you need to model the inverse of the modulation function.
Please see the code below (for p=2):
prev=0;
for i = 1:numel(d_k)
if i <= 1
x_ind = d_k(i) + prev;
else
x_ind = d_k(i) + x_hat(i-1) + prev;
prev = x_hat(i-1);
end
x_hat(i) = x_ind;
end
Here d_k is the modulated signal and x_hat is the demodulated signal.
Below is the full script integrated with your modulation code:
%% Initialize the variables
p=2;
x_k = [1 2 3 4 5]; % Original Signal
d_k = zeros(1,length(x_k)); % Modulated Signal
x_hat = zeros(1,length(x_k)); % Demodulated Signal
%% Modulation
% x_k is the message signal
x_kdelay = [0 x_k(1:end-1)]; %Delay by 1 unit
if p == 1
d_k = x_k - x_kdelay;
elseif p == 2
for i5 = 1:numel(x_k)
if i5 <=1
d_k(i5) = x_k(i5) - (x_kdelay(i5));
else
d_k(i5) = x_k(i5) - (x_kdelay(i5)+x_kdelay(i5-1));
end
end
end
d_k
%% Demodulation
prev = 0;
if p == 1
for i3 = 1:numel(d_k)
x_hat(i3) = prev + d_k(i3);
prev = x_hat(i3);
end
% Function that is required
elseif p==2
for i = 1:numel(d_k)
if i <= 1
x_ind = d_k(i) + prev;
else
x_ind = d_k(i) + x_hat(i-1) + prev;
prev = x_hat(i-1);
end
x_hat(i) = x_ind;
end
end
x_hat
You can see that the original signal is reproduced. You can change the value of p to check the signal is reproduced for p=1 as well.
Note that I have made a small change in demodulation code for p=1 as well. This was because in the code provided by you the size of array x_hat was changing for each loop iteration. I have preallocated the space to make it faster.
