Suppose we want to fit a Fourier series to a dataset. As an example, let's take a step function:
f(x) = \begin{cases} 0 & \text{if}\quad - \pi < x \leq 0 \\
1 & \text{if}\quad 0 < x < \pi
\end{cases}
In the example below, we will attempt to fit this with a Fourier Series of order n=3.
y(x) = a_0 + \sum_{i=1}^n a_i cos(i \omega x)
+ \sum_{i=1}^n b_i sin(i \omega x)
.. literalinclude:: ../../examples/fourier_series.py
:language: python
This code prints:
{y: a0 + a1*cos(w*x) + a2*cos(2*w*x) + a3*cos(3*w*x) + b1*sin(w*x) + b2*sin(2*w*x) + b3*sin(3*w*x)}
Parameter Value Standard Deviation
a0 5.000000e-01 2.075395e-02
a1 -4.903805e-12 3.277426e-02
a2 5.325068e-12 3.197889e-02
a3 -4.857033e-12 3.080979e-02
b1 6.267589e-01 2.546980e-02
b2 1.986491e-02 2.637273e-02
b3 1.846406e-01 2.725019e-02
w 8.671471e-01 3.132108e-02
Fitting status message: Optimization terminated successfully.
Number of iterations: 44
Regression Coefficient: 0.9401712713086535
