Fourier Series Square Wave Value

Problem

The square wave of amplitude 1 has the Fourier series (4/pi) * sum over odd k of sin(k*x) / k.

Evaluate the partial sum including all odd k from 1 through n at the point x (radians). Near the jump the partial sum overshoots (the Gibbs phenomenon).

Hint

Iterate k = 1, 3, 5, ... up to n and accumulate sin(k x) / k.

Test cases

case 1

in: [0,99]

expected: 0

case 2

in: [1.5707963267948966,99]

expected: 0.9936344385781744

case 3

in: [0.5235987755982988,9]

expected: 0.9559401661265586

case 4

in: [3.141592653589793,99]

expected: 0

Starter codePython

def square_wave_value(x, n):
    # Your code here
    pass

4 test cases · run your code against them in the editor