FFT and Fourier series formulas from CSV data file

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Seweryn 2023-10-31

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https://ww2.mathworks.cn/matlabcentral/answers/2040741-fft-and-fourier-series-formulas-from-csv-data-file

评论： Walter Roberson 2023-10-31

Hi guys, I'm struggling with a problem. I obtained the rms values for ch1 (voltage) and ch2 (current) and performed an FFT analysis in simulink (as you can see in pdf file), but I wonder if I can get the Fourier series formulas for each waveform in Matlab? Values start at line 22 in .csv file (A22:C10021)

I would be delighted to any help.

Kind regards,

Seweryn

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Answer 1

Walter Roberson 2023-10-31

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https://ww2.mathworks.cn/matlabcentral/answers/2040741-fft-and-fourier-series-formulas-from-csv-data-file#answer_1343816

移动：Walter Roberson 2023-10-31

在 MATLAB Online 中打开

tek0005.csv

filename = 'tek0005.csv';

data = readmatrix(filename, 'HeaderLines', 21);

time = data(:,1);

T = mean(diff(time));

Fs = 1./T;

L = height(time);

freqs = Fs/L*(0:L-1);

ch1 = data(:,2);

ch2 = data(:,3);

F1 = fft(ch1);

F2 = fft(ch2);

tiledlayout('flow');

nexttile();

plot(freqs, abs(F1)); title('ch1');

xlabel("f (Hz)"); ylabel("|fft(ch1)|")

nexttile();

plot(fftshift(abs(F1))); title('shifted ch1');

nexttile();

plot(freqs, abs(F2)); title('ch2');

xlabel("f (Hz)"); ylabel("|fft(ch2)|")

nexttile();

plot(fftshift(abs(F2))); title('shifted ch2');

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Seweryn 2023-10-31

编辑：Seweryn 2023-10-31

Hi @Walter Roberson, thank you so much for your help, I'm also wondering if we can get a trigonometric Fourier series with appropriate coefficients for each waveform? Something like the picture below. Thank you in advance!

Walter Roberson 2023-10-31

https://en.m.wikipedia.org/wiki/Euler%27s_formula

now consider exp(i*x + c) where c is real.

Each entry in the fft output is a complex number so using the equivalence you can separate into sin and cos components.

There will be thousands of these components unless you are willing to say that if abs() of a component is less than a tolerance then you want to consider the component to be effectively 0.

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