CoCalc -- Fourier Series.ipynb

Jupyter notebook Fourier Series.ipynb

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Kernel: Python 3

In [1]:

import matplotlib.pyplot as plt
from numpy import pi,sin,linspace,zeros,arange,cos
from ipywidgets import interact
%matplotlib inline

The fourier series for a square wave is

f(x) = \frac{4}{\pi} \sum^\infty_{n=odd} \frac{1}{n}\sin \left(\frac{n\pi x}{L} \right)

Let us explore how this summation converges

In [2]:

def square_wave(N = 1,L = 5,num_points = 200):
    x = linspace(-4*pi,4*pi,num_points)
    y = zeros(num_points)
    for n in arange(1,N+1,2):
        y = y + (1.0/n * sin(n*pi*x/L))
    y = y * 4.0/pi
    plt.plot(x,y)

In [3]:

square_wave(N=5,L=5)

Out[3]:

An interactive version of the above:

In [4]:

interact(square_wave,N=(1,50,2),L=5,points=200)

Out[4]:

In [ ]:

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