The formulae for the Fourier series coefficients contain f(x), e.g.
$$ b_n = \frac 1\pi \int_{-\pi}^\pi f(x)sin(nx)dx $$
But if I don't know what f(x) is, e.g.
or
then how can I get the coefficients?
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1\$\begingroup\$ You could use a numerical approach. Capture the data to digital form, then compute the discrete Fourier transform. \$\endgroup\$– user57037Commented Sep 6, 2015 at 18:26
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1\$\begingroup\$ You can still use algebra - just approximate each section to a part of a sinewave or straight line or whatever and integrate in sections \$\endgroup\$– Andy akaCommented Sep 6, 2015 at 19:01
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1\$\begingroup\$ If you do not know what \$f(x)\$ is then you can't compute the fourier coefficients. \$\endgroup\$– Vladimir CraveroCommented Sep 6, 2015 at 19:48
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\$\begingroup\$ f(x) represents the waveshape of your "weird waveform". If it makes you feel better, you can replace the variable "x" with a "t" for time but he result is the same. \$\endgroup\$– BarryCommented Sep 6, 2015 at 21:13
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\$\begingroup\$ Andy, if you write that as an 'answer', I'll 'accept' it. \$\endgroup\$– John SmallberriesCommented Sep 12, 2015 at 14:34
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2 Answers
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If the periodic time can be determined by inspection, you can proceed numerically and use Fourier Series analysis. In this case, Fourier Series is probably better than Fourier Transform, since: the FT is not particularly accurate in the calculation of phase angles; FS is potentially faster than FT (or FFT); it's preferable to use all available a-priori knowledge of a signal, rather than discard it; the FS can be derived quite simply using, e.g., Excel, whereas calculating the FT is not as straightforward, so you'd probably need access to a package.
If the waveform is not periodic, or if the periodic time is not easily discernible (eg the fundamental frequency may not be present in the signal), then the FT is indicated.
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If you have a symbolic expression, apply the formula for the transform.
If you have an unknown waveform, you can use an FFT algorithm. Just capture it with a digital scope, then throw it into Excel
answered Sep 6, 2015 at 20:45