Reversing a function at the Receiver side

Question

Abdelrhman Abdelfatah 2022-12-9

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1874657-reversing-a-function-at-the-receiver-side

回答： Yash 2023-8-29

Hello all, I have the following code:

%%%%%%Reciver

intial_value = 0;

x_hat = [];

%% Predictator

%%OLD

if p == 1

for i3 = 1:numel(d_k)

x_ind = intial_value +dq_tx(i3);

x_hat = [x_hat x_ind];

intial_value = x_ind;

end

which is a demodulation at the reciever side, from the following 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;

Now I wrote this function to modulate the input signal in the case of p=2

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

And I want to write a similar function at the reciever side that de-modulates that, any help would be apprechiated.

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Answer 1

Yash 2023-8-29

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https://ww2.mathworks.cn/matlabcentral/answers/1874657-reversing-a-function-at-the-receiver-side#answer_1295826

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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 
d_k = 1×5
     1     1     0    -1    -2
%% 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
x_hat = 1×5
     1     2     3     4     5

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.