Add fourier problem

fourier.py

@@ -0,0 +1,47 @@
+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()

functions.py

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+# P372-PS06-functions.py
+# Find your function and cut and paste into your program.
+# -----------------------------------------------------------
+waveName = "square wave"  # Your function
+
+g = [0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+     1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+     0.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,
+     -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0]
+# -----------------------------------------------------------
+waveName = "2 cycle square "  # Your function
+
+g = [0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+     0.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,
+     0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+     0.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0]
+# -----------------------------------------------------------
+waveName = "Impulse"  # Your function
+
+g = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+     1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+     0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+     0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
+# -----------------------------------------------------------
+waveName = "Wide Impulse"  # Your function
+
+g = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+     0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+     1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+     0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
+# -----------------------------------------------------------
+waveName = "Impulse Pair"  # Your function
+
+g = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+     1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+     0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+     -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
+# -----------------------------------------------------------
+waveName = "Triangle Wave"  # Your function
+
+g = [0.0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875,
+     1.0, 0.875, 0.75, 0.625, 0.5, 0.375, 0.25, 0.125,
+     0.0, -0.125, -0.25, -0.375, -0.5, -0.625, -0.75, -0.875,
+     -1.0, -0.875, -0.75, -0.625, -0.5, -0.375, -0.25, -0.125]
+# -----------------------------------------------------------
+waveName = "Sawtooth"  # Your function
+
+g = [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7,
+     0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5,
+     0.0, -1.5, -1.4, -1.3, -1.2, -1.1, -1.0, -0.9,
+     -0.8, -0.7, -0.6, -0.5, -0.4, -0.3, -0.2, -0.1]
+# -----------------------------------------------------------
+waveName = "Wide Pulse Pair"  # Your function
+
+g = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0,
+     1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+     0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0,
+     -1.0, -1.0, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0]
+# -----------------------------------------------------------
+waveName = "Step Sawtooth"  # Your function
+
+g = [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]
+# -----------------------------------------------------------