How can I add distance to signals and how can I determine the locations of signals?

please

I have two sources for sending signals, where x1 represents the signal from the first source and x2 represents the signal from the second source :

where :

w1: First Angular Frequncy (rad / sec) and frequncy 40 KHZ.

W2: Second Angular Frequncy (rad / sec) and frequncy 60 KHZ.

n: Number of samples

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I have this code, how can I add the following to it?

1. How can I add the distance to x1 and x2 and find the distance between them ?
2. How can I find location x1 and location x2 ?
3. Plot Magnitude of FFT with frequencies ?

Please rewrite the code correctly to get the above results.

    clear all
    clc
    close all
    
    % Define all the parameters.
    
    % Frequncy for wave one(KHZ).
    f1 = 40e6 ;  
    % Frequncy for wave two(KHZ).
    f2 = 60e6 ;
    
    % The speed of light in vacuum (m/sec).
    c = 3e8 ;
    
    % Wavelength for wave one(m).
    h1 = c / f1 ;
    % Wavelength for wave two(m).
    h2 = c / f2 ;
    
    
    % Imaginary part.
    j=sqrt(-1);
    
    % Initialize the vector to store the values.
    X = zeros(1, 20);
    
    % Make for loop (where n: number of samples).
    for n = 1:20;
        
        x1=exp(j*h1*n);
        x2=exp(j*h2*n);
        X(n) = x1 + x2;
    
    end
    
    % Compute FFT.
    Y = fft(X, 256);
    
    % Compute Magnitude FFT
    Y1 = abs(Y);
    plot( Y1 );
    grid on
    title('Magnitude of FFT Spectrum of X(N)', 'FontSize',12,'Color','k');

Answer 1

[Suraj Kumar]

Hi Muhammad,

To incorporate distance into signals, find their locations and plot the FFT magnitude, you can refer to the following steps and attached code snippets:

1. The phase shift due to distance was incorporated into the signals by multiplying by the term “exp (-j * 2 * pi * f * d / c)”. This term accounts for the phase delay introduced by the distance the signal travels.

x1 = exp(j * h1 * n) * exp(-j * 2 * pi * f1 * d1 / c); 
x2 = exp(j * h2 * n) * exp(-j * 2 * pi * f2 * d2 / c); 
X(n) = x1 + x2; 

2. The signal locations were determined by distances (d1) and (d2) and printed to the console to indicate positions of (x1) and (x2).

% Display locations 
disp(['Location of x1: ', num2str(d1), ' meters']); 
disp(['Location of x2: ', num2str(d2), ' meters']); 

3. The FFT of the combined signal was computed, and its magnitude was plotted against a normalized frequency axis, providing a clear visualization of the signal's frequency components.

% Compute FFT. 
Y = fft(X, 256); 
% Compute Magnitude FFT 
Y1 = abs(Y); 
% Frequency axis for plotting 
Fs = 1;  
f = (0:255) * (Fs / 256); 
% Plot Magnitude of FFT with frequencies 
figure; 
plot(f, Y1); 
grid on; 
title('Magnitude of FFT Spectrum of X(N)', 'FontSize', 12, 'Color', 'k'); 
xlabel('Frequency (Hz)', 'FontSize', 12); 
ylabel('Magnitude', 'FontSize', 12); 

You may refer to the output below for a clearer understanding:

For more information on “fft” and ”abs” function, kindly go through the documentation below:

• https://www.mathworks.com/help/matlab/ref/fft.html
• https://www.mathworks.com/help/matlab/ref/abs.html

Hope it helps!