Python separate sin waves Fourier Transform

Question

I'm currently trying to make a sin wave separator, at replit.com. However, I am running it, and the bottom graph is off. There should be on spike, but there are multiple in the area. It is using the function e ^ (-2pi * i * frequency * the height of the sin wave). Can anyone help me? The math I am basing it off of is this video. Thank you!

for i in range(180):
  height.append(cos(2 * i * const))
center = (0 + 0j)

centers = []
centers2 = []
centers3 = []

for a in range(180):
  f = a * const
  center = (0 + 0j)
  for a, i in enumerate(height):
    center += -i * e**(-2 * pi * 1j * f * a)
    #maybe fix equation? It looks off...
  center *= 1/(a)
  centers3.append(sqrt(center.real ** 2 + center.imag **2))
  centers.append(center.real)
  centers2.append(center.imag)

Answer 1

The thing in the exponential has a factor of 2 pi too much in it. So you could say that f is a factor of 2 pi too high, or that the factor of 2 pi does belong in f but then it shouldn't be repeated in the exponential, either way it's in there twice while it should be in there once.

Changed code, plus minor other edits:

from math import cos, pi, e, sqrt, atan2
import matplotlib.pyplot as plt
import numpy as np

const = 2 * pi/180
height = []
for i in range(180):
  height.append(cos(2 * i * const))

amplitudes = []
phases = []

print(90 / 180, 90 * const)

for a in range(180):
  f = a / 180
  center = (0 + 0j)
  for index, sample in enumerate(height):
    center += sample * e**(-2 * pi * 1j * f * index)
    # fixed equation
  amplitudes.append(sqrt(center.real ** 2 + center.imag **2))
  phases.append(atan2(center.imag, center.real))

x = np.linspace(0, np.pi, 180)
y = height

fig, ax = plt.subplots(2,2)
ax[0,0].plot(x, y)
ax[1,0].plot(x, amplitudes)
ax[1,1].plot(x, phases, 'orange')
#ax[0,1].plot(x, centers3, 'orange')
plt.show()

Output: