Fourier Analysis

Overview


This example shows calculating a Fourier series expansion for the function {% y = x^2 %}

Fourier Series Expansion


{% a_0 = 2 \pi ^2 / 3 %}
{% a_n = 4(-1)^n/n^2 %}

Approximation Function


The Fourier series can be used to approximate other functions. As an example, once one has computed the first 3 cosine coefficients, once could write a function that approximates the target function as follows. 


let approx = x => {
  return 0.5 * a0 + a1 * Math.cos(x) + a2 * Math.cos(2*x);
}


Then, we can chart the results by creating a set of samples as in the following. 


let samples = $from(-1 * Math.PI, Math.PI, 1000).map(p=>{
  return {
    x:p,
    y:approx(p)
  };											
})


The following is an example of approximating a parabola {% y = x^2 %} using the first 3 Fourier cosine.

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