Pretty much all of Fall 2024

7th-Semester-Fall-2024/ECOMMS/exams/exam-1/problem-1.py

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+import numpy as np
+
+f_1 = 5 
+f_2 = 5E3
+omega_1 = 2*np.pi*f_1
+omega_2 = 2*np.pi*f_2
+
+A_c = 10
+a = 1
+
+def m(t):
+    return 0.2*np.cos(omega_1*t) + 0.8*np.cos(omega_2*t)
+
+def dm_dt(t):
+    return -0.2*omega_1*np.sin(omega_1*t) - 0.8*omega_2*np.sin(omega_2*t)
+
+def ddm_dtt(t):
+    return -0.2*omega_1**2*np.cos(omega_1*t) - 0.8*omega_2**2*np.cos(omega_2*t)
+
+def g(t):
+    return A_c + A_c*m(t)
+
+# first derivative of g(t)
+def dg_dt(t):
+    return A_c*dm_dt(t)
+
+# second derivative of g(t)
+def ddg_dtt(t):
+    return A_c**2*ddm_dtt(t)
+
+# use Newton's method to find the maximum of the function
+def newton_method(t):
+    for i in range(10):
+        t = t-dg_dt(t)/ddg_dtt(t)
+    print("Newton method:", t, np.min(m(t)))
+    return np.min(g(t))
+
+# Sample g(t) at the maxima and minima of the carrier signal
+def sample_method():
+    f_s = 4*max(f_1, f_2)
+    T_s = 1/f_s
+    T_0 = 1/min(f_1, f_2)
+    
+    t = np.arange(0,T_0,T_s)
+
+    t = t[np.argmin(m(t))]
+    print("Sampling method:", t, m(t))
+    return t
+
+if __name__ == '__main__':
+    newton_method(0.1)

7th-Semester-Fall-2024/ECOMMS/exams/exam-1/problem-2.py

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+import numpy as np
+import scipy as sp
+import matplotlib.pyplot as plt
+
+A_c = 1
+
+f_1 = 500
+T_1 = 1/f_1
+omega_1 = 2*np.pi*f_1
+
+f_c = 20000
+T_c = 1/f_c
+omega_c = 2*np.pi*f_c
+
+def m(t):
+    return 2*np.cos(2*omega_1*t) + 3*np.cos(3*omega_1*t)
+
+def s(t):
+    return A_c*m(t)*np.cos(omega_c*t)
+
+f_s = 40*f_c
+T_s = 1/f_s
+t = np.arange(0,T_1,T_s)
+
+plt.plot(t,s(t))
+plt.plot(t,m(t))
+plt.show()
+
+S = sp.fft.fft(s(t))[35:45]
+f = t*f_s/T_1
+f = f[35:45]
+for i in range(len(f)):
+    print(f[i], S[i].real)
+
+plt.stem(f,S.real/1600)
+plt.show()
+