Determine the direction of travelling waves in Fourier Analysis

% I am conducting a FFT analysis and i I observed that there is travelling
% wave. Please, how do I determine the direction of the travelling waves? 

% Compute the phase of the FFT: theta_phase = angle(Ytheta);

% Compute the mean phase difference: p = polyfit(f, theta_phase, 1);
% slope = p(1); % The slope of the phase vs. frequency plot
% Store the mean phase difference: mean_phase_diff(i) = slope;
% Then I test the mean_phase_diff(i) > 0 implies rightward direction or if
% mean_phase_diff(i) < 0 leftward direction. I am wondering if there is a
% better way or function to do this. 



clear
%close all

pars.W = 20e-6;         
pars.D = 2e-6;          

% time discretisation - start, step and end
t = 0:0.025:5;

% Extract theta data 
loaded_data = load('thetam.mat'); 
thetam = loaded_data.thetam;  

% Sample frequency 
Fs = 1/(t(2) - t(1));                    

% Number of samples
L = length(t);   

% Number of ramp slopes
num_ramp_slopes = size(thetam, 1);

% Frequency vector for FFT
f = (-L/2 : L/2-1) * (Fs / L);

% Loop through each ramp_slope
for i = 1:num_ramp_slopes
    % Extract the theta data for the current ramp_slope
    theta_data = thetam(i, :);
    
    % Compute the FFT of the theta data
    Ytheta = fft(theta_data);
    
    % Shift zero frequency component to center
    Ytheta = fftshift(Ytheta);
end

% Plot the magnitude of the FFT for the first ramp_slope
fig1 = figure;
plot(f, abs(fftshift(fft(thetam(1, :)))), 'LineWidth', 0.8);
xlabel('Frequency (Hz)');
ylabel('Magnitude');
title('FFT Magnitude for Ramp Slope 1');
xlim([-Fs/2 Fs/2]);
grid on;

Answer 1

[Ayush]

Hi there

You can use the approach of analyzing the phase slope to determine the direction of traveling waves using FFT as:

clear
%close all

% Parameters
pars.W = 20e-6;         
pars.D = 2e-6;          

% Time discretization: start, step, and end
t = 0:0.025:5;

% Load theta data
loaded_data = load('thetam.mat'); 
thetam = loaded_data.thetam;  

% Sample frequency
Fs = 1/(t(2) - t(1));                    

% Number of samples
L = length(t);   

% Number of ramp slopes
num_ramp_slopes = size(thetam, 1);

% Frequency vector for FFT
f = (-L/2 : L/2-1) * (Fs / L);

% Initialize storage for mean phase differences
mean_phase_diff = zeros(1, num_ramp_slopes);

% Loop through each ramp_slope
for i = 1:num_ramp_slopes
    % Extract the theta data for the current ramp_slope
    theta_data = thetam(i, :);
    
    % Compute the FFT of the theta data
    Ytheta = fft(theta_data);
    
    % Shift zero frequency component to center
    Ytheta = fftshift(Ytheta);
    
    % Compute the phase of the FFT
    theta_phase = angle(Ytheta);
    
    % Compute the mean phase difference using linear fit
    p = polyfit(f, theta_phase, 1);
    slope = p(1); % The slope of the phase vs. frequency plot
    
    % Store the mean phase difference
    mean_phase_diff(i) = slope;
    
    % Determine the direction based on the slope
    if slope > 0
        direction = 'rightward';
    else
        direction = 'leftward';
    end
    
    fprintf('Ramp Slope %d: Mean Phase Difference = %.3f, Direction = %s\n', i, slope, direction);
end

% Plot the magnitude of the FFT for the first ramp_slope
fig1 = figure;
plot(f, abs(Ytheta), 'LineWidth', 0.8);
xlabel('Frequency (Hz)');
ylabel('Magnitude');
title('FFT Magnitude for Ramp Slope 1');
xlim([-Fs/2 Fs/2]);
grid on;

I hope this helps!