how to plot the fundamental harmonic wave from given Data

I have exported data to an Excel spreadsheet where the x-axis is represented by theta (in radians) and y-axis is the flux density distribution. How can I plot the fundamental harmonic wave from this wave data?

i used the same code as in https://de.mathworks.com/matlabcentral/answers/2049232-plot-the-fundamental-harmonic-wave,

but it does not work. the mat file is attached.

%%%%%%%%%%%%% main code %%%%%%%%%%%%%%%%%

% 2nd order extraction (DFT)

order = 2;

% model fit : X = A*cos(order*theta) + B*sin(order*theta) + C

C = mean(y);

y = y-C;

n = numel(theta);

A = 2/n*trapz(y.*cos(order*theta));

B = 2/n*trapz(y.*sin(order*theta));

yfit = A*cos(order*theta) + B*sin(order*theta) + C;

% plot

figure(1),

plot(theta, y, 'b',theta, yfit, 'r')

legend('data','model fit');

[akshatsood]

Hi @Abdullah,

Could you please elaborate on what "does not work" with the attached code.

Answer 1

[Mathieu NOE]

@Abdullah

hello

here you have 4 periods of signal for theta range of 2pi , so order = 4

load('FluxDensity.mat')
%%%%%%%%%%%%% main code %%%%%%%%%%%%%%%%%
% 4th order extraction (DFT)
order = 4;
% model fit : X = A*cos(order*theta) + B*sin(order*theta) + C
C = mean(y);
y = y-C;
n = numel(theta);
A = 2/n*trapz(y.*cos(order*theta));
B = 2/n*trapz(y.*sin(order*theta));
yfit = A*cos(order*theta) + B*sin(order*theta) + C;
% plot
figure(1),
plot(theta, y, 'b',theta, yfit, 'r')
legend('data','model fit');

[Abdullah]

Great!. it worked!

[Abdullah]

@Mathieu NOE

Hello Mathieu,

could you please just check the new attached file" FluxDensity_new.mat" and see if you could plot the first harmonic? because the use the same code and change the order to 1 but did not work.

thank you in advance!

[Mathieu NOE]

hello again

it didn't work because the code assumes theta is given in rads as it was in the previous case

your new file gives theta in degrees so you have to convert first in radians

load('FluxDensity_new.mat')
% y = Br_noLoad;
y = Br_WithLoad;
theta = theta*pi/180;

%%%%%%%%%%%%% main code %%%%%%%%%%%%%%%%%
%  order extraction (DFT)
order = 1;
% model fit : X = A*cos(order*theta) + B*sin(order*theta) + C
C = mean(y);
y = y-C;
n = numel(theta);
A = 2/n*trapz(y.*cos(order*theta));
B = 2/n*trapz(y.*sin(order*theta));
yfit = A*cos(order*theta) + B*sin(order*theta) + C;
% plot
figure(1),
plot(theta, y, 'b',theta, yfit, 'r')
legend('data','model fit');
xlable('theta (rad)');

Answer 2

[akshatsood]

Hi @Abdullah,

I would like to share insights on alternative approach to plot the fundamental harmonic wave of your data in MATLAB leveraging the bandpass() and fft() function. This approach involves first identifying the fundamental frequency of your signal using the Fourier Transform (via fft()), and then filtering around that frequency with bandpass() to isolate the fundamental harmonic.

Step 1: Prepare the Signal for FFT

First, you need to convert theta to a time or space domain that makes sense for FFT, which requires evenly spaced samples. Assuming theta is evenly spaced, sampling frequency can be computed as follows

Fs = 1 / mean(diff(theta)); % Sampling frequency

Step 2: Use FFT to Find the Fundamental Frequency

L = length(y); % Length of the signal

Y = fft(y); % Compute the FFT

P2 = abs(Y/L); % Two-sided spectrum

P1 = P2(1:L/2+1); % Single-sided spectrum

P1(2:end-1) = 2*P1(2:end-1);

f = Fs*(0:(L/2))/L; % Frequency domain


% Find the fundamental frequency (ignoring DC component)

[~, I] = max(P1(2:end)); % Index of max peak

fundamentalFreq = f(I+1); % Fundamental frequency, offset by 1 due to ignoring DC

Step 3: Use bandpass() to Isolate the Fundamental Harmonic

Let us center this around fundamentalFreq and specify a small bandwidth. Make sure y is suitable for bandpass()

bw = fundamentalFreq * 0.1; % bandwidth: 10% of the fundamental frequency

filteredSignal = bandpass(y, [fundamentalFreq-bw, fundamentalFreq+bw], Fs);

Step 4: Plot the Original and Filtered Signals

figure;

plot(theta, y); % Original signal

hold on;

plot(theta, filteredSignal, 'LineWidth', 2); % Filtered signal showing fundamental harmonic

legend('Original Data', 'Fundamental Harmonic');

xlabel('\theta (radians)');

ylabel('Flux Density Distribution');

title('Fundamental Harmonic Isolation');

I hope this helps.

[Abdullah]

Hello akshatsood,

Thank you for your detailed explanaition.

i have expected that the amplitude of the fundamental harmonic should be near to the original, in this solution seams that it is very low which i did not expect, it is attenuating in the fourth cycle.

i really wondering that Matlab does not provide easy solution.