48 lines
1.4 KiB
Python
48 lines
1.4 KiB
Python
|
import numpy as np
|
||
|
|
import pylab as pl
|
||
|
|
|
||
|
|
n_period_points = 32 # Number of points in period
|
||
|
|
dx = 1.0 / n_period_points
|
||
|
|
x_vals = np.arange(0.0, 1.0, dx) # This is the interval to be analyzed
|
||
|
|
|
||
|
|
waveName = "Step Sawtooth"
|
||
|
|
|
||
|
|
wave_y_vals = [0.0, 0.0, 0.5, 0.5, 0.5, 0.5, 1.0, 1.0,
|
||
|
|
1.0, 1.0, 1.5, 1.5, 1.5, 1.5, 2.0, 2.0,
|
||
|
|
-2.0, -2.0, -1.5, -1.5, -1.5, -1.5, -1.0, -1.0,
|
||
|
|
-1.0, -1.0, -0.5, -0.5, -0.5, -0.5, 0.0, 0.0]
|
||
|
|
|
||
|
|
print("PHY372 Spring 2024 Problem Set 6")
|
||
|
|
print("Fourier analysis and re-synthesis of a", waveName)
|
||
|
|
print("P372-PS06-FourierSeriesTemplate")
|
||
|
|
print("Matthew Oros Feb 2024")
|
||
|
|
|
||
|
|
m_vals = np.arange(0, n_period_points // 2)
|
||
|
|
|
||
|
|
s_list: list[np.ndarray] = []
|
||
|
|
c_list: list[np.ndarray] = []
|
||
|
|
for m in m_vals:
|
||
|
|
s_list.append(np.sin(m * 2 * np.pi * x_vals))
|
||
|
|
c_list.append(np.cos(m * 2 * np.pi * x_vals))
|
||
|
|
|
||
|
|
a_coeffs: list[float] = []
|
||
|
|
for c in c_list:
|
||
|
|
a_coeffs.append(2.0 * np.dot(wave_y_vals, c) * dx)
|
||
|
|
|
||
|
|
b_coeffs: list[float] = []
|
||
|
|
for s in s_list:
|
||
|
|
b_coeffs.append(2.0 * np.dot(wave_y_vals, s) * dx)
|
||
|
|
|
||
|
|
y_vals = np.zeros(n_period_points)
|
||
|
|
for i in range(len(m_vals)):
|
||
|
|
y_vals += a_coeffs[i] * c_list[i] + b_coeffs[i] * s_list[i]
|
||
|
|
|
||
|
|
pl.plot(x_vals, y_vals, 'r', linewidth=2.0)
|
||
|
|
pl.plot(x_vals, wave_y_vals, linewidth=1.0)
|
||
|
|
pl.axis((0.0, 1.0, -2.5, 2.5))
|
||
|
|
pl.xlabel('position x')
|
||
|
|
pl.ylabel('function')
|
||
|
|
pl.title('Fourier re-synthesis of ' + waveName)
|
||
|
|
|
||
|
|
pl.show()
|