Hello everyone,
Today I decided to refresh my knowledge of Fourier Expansion. I tried to
use Sympy but I'm not sure if the result is correct or if I did something
wrong, so I need a fresh pair of eyes on this :)
I was following the "Fourier Series of a Square Wave" in the Wolfram
documentation [1], and I compare the result with Sympy. Here is the code
and the picture.
x, n = symbols("x, n")
N = 10
expr = 2 * (Heaviside(x / 2) - Heaviside(x / 2 - 1)) - 1
fs = expr.fourier_series()
wolfram = 4 / pi * sin(n * pi * x / 2) / n
wolfram_expr = 0
for i in range(1, N + 1):
if i % 2 != 0:
wolfram_expr += (4 / pi * sin(n * pi * x / 2) / n).subs(n, i)
plot(expr, fs.truncate(N), wolfram_expr, (x, -5, 5))
[image: Figure 70.png]
Did I do something wrong?
Thanks for you time! :)
[1] https://mathworld.wolfram.com/FourierSeriesSquareWave.html
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