Pretty much all of Fall 2024

7th-Semester-Fall-2024/ECOMMS/homework/homework-2/problem-2.py

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+import numpy as np
+
+f_m = 0.2
+f_c = 2*f_m
+A_c = 1
+a = 1
+
+def g(t):
+    return A_c*np.cos(2*np.pi*f_m*t) + A_c*np.cos(2*np.pi*f_c*t)
+
+# first derivative of g(t)
+def dg_dt(t):
+    return -(2*np.pi*f_m)*A_c*np.sin(2*np.pi*f_m*t) + -(2*np.pi*f_c)*A_c*np.sin(2*np.pi*f_c*t)
+
+# second derivative of g(t)
+def ddg_dtt(t):
+    return -(2*np.pi*f_m)**2*A_c*np.cos(2*np.pi*f_m*t) + -(2*np.pi*f_c)**2*A_c*np.cos(2*np.pi*f_c*t)
+
+# use Newton's method to find the maximum of the function
+def newton_method(t):
+    for i in range(3):
+        t = t - dg_dt(t)/ddg_dtt(t)
+        print(f"Iteration {i+1}: {t}\t{g(t)}")
+
+def dc_dt(t):
+    return A_c*a*np.pi*f_c*np.cos(2*np.pi*f_c*t)
+
+if __name__ == '__main__':
+    T_c = 1/f_c
+    t_min = T_c/2
+    newton_method(t_min)
+    
+    newton_method(0)