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Fourier Series

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Fourier series of Sawtooth Function

Fourier series (n=9) representing a sawtooth function.

This is a sample Fourier series used to represent a Ggb.gifsawtooth function.

The series was built using the Sum[] command together with the Sequence[] command. In addition, the series formula is presented as text using LaTeX.SEO DallasFLAS INFORMASI TEKNOLOGI kumpulan i

The .ggb file is was developed collaboratively on the GeoGebra forum: "How to Input Long Formulae (as Fourier terms)"


Fourier series of arbitrary functions

Fourier series (n=9) representing a step function.

This is an initial attempt at a Fourier series generator for arbitrary functions. Ggb.gifFourier series

To use this tool, enter your function named f(x) in the Input Bar at the bottom of the applet. For example,

  • f(x) = x \, ... sawtooth function
  • f(x) = \mathrm{If}[x<0, 0, 3] \, ... step function
  • f(x) = \mathrm{If}[x<0, -x, x] \, ... triangle function

The domain of the defining function is given by the interval [xa,xb], thus the period is p = xb − xa. We also define the wavenumber k = 2π / p.

Among the values displayed in the Algebra window are the lists "a" and "b", which are the coefficients of cosine and sine functions, respectively.

a_n = \frac{2}{p}\int_{xa}^{xb} f(x) \cos(nkx) \, dx, \quad n \ge 1;\qquad a_0 = \frac{1}{p}\int_{xa}^{xb} f(x) \, dx
b_n = \frac{2}{p}\int^{xb}_{xa} f(x) \sin(nkx) \, dx, \,\quad n \ge 1
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