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Muhammad Salem on 7 Nov 2023
Answered: Suraj Kumar about 3 hours ago
Open in MATLAB Online
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
------------------------------------------------------------------------------------------------
I have this code, how can I add the following to it?
- How can I add the distance to x1 and x2 and find the distance between them ?
- How can I find location x1 and location x2 ?
- 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');
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Answers (1)
Suraj Kumar 2 minutes ago
Open in MATLAB Online
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!
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