lab1q3 discrete version

8th-Semester-Spring-2025/clinic-consultant/labs/lab-1/lab1q1.py

@@ -1,6 +1,17 @@
+"""
+ECE 09351 - Digital Signal Processing
+Lab 1 Question 1
+
+Translated from MATLAB by Aidan Sharpe
+Last Modified: January 16, 2025
+"""
+
+
 import numpy as np
 import matplotlib.pyplot as plt
 
+
+
 def main():
     f_s = 100                   # Sample frequency [Hz]
     T_s = 1/f_s                 # Sample period [s]
@@ -18,5 +29,7 @@ def main():
 
     plt.show()                  # Show the plot
 
+
+
 if __name__ == "__main__":
     main()

8th-Semester-Spring-2025/clinic-consultant/labs/lab-1/lab1q2.py

@@ -0,0 +1,36 @@
+"""
+ECE 09351 - Digital Signal Processing
+Lab 1 Question 2
+
+Translated from MATLAB by Aidan Sharpe
+Last Modified: January 16, 2025
+"""
+
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+
+def main():
+    f_sweep = np.arange(1,25)*np.pi                             # Angular frequency sweep from pi to 24*pi
+    f_max = np.max(f_sweep)                                     # Maximum frequency in the frequency sweep
+    f_s = 2*f_max                                               # Sample frequency at twice maximum
+    T_s = 1/f_s                                                 # Sampling period
+
+    E = np.empty_like(f_sweep)                                  # Array to store energy calculations
+    for i, f in enumerate(f_sweep):                             # Loop over all frequencies in sweep
+        W = np.arange(0, f, T_s)                                # Define the variable of integration
+        x = np.sinc(0.5*W/np.pi)                                # np.sinc(0.5*W/np.pi) = sinc(0.5*W)
+        E[i] = np.sum(x**2 * T_s)/np.pi                         # Integrate x^2, with dt = T_s
+
+    plt.stem(f_sweep, E)                                        # Plot energy at each frequency in sweep
+    plt.hlines(0.99, f_sweep[0], f_sweep[-1], colors="red")     # Red horizontal line at 99% total energy
+    plt.xlabel("Angular frequency")
+    plt.ylabel("Signal energy")
+    plt.show()
+
+
+
+if __name__ == "__main__":
+    main()

8th-Semester-Spring-2025/clinic-consultant/labs/lab-1/lab1q3.py

@@ -0,0 +1,48 @@
+"""
+ECE 09351 - Digital Signal Processing
+Lab 1 Question 3
+
+Translated from MATLAB by Aidan Sharpe
+Last Modified: January 17, 2025
+"""
+
+import numpy as np
+import scipy as sp
+import matplotlib.pyplot as plt
+
+
+def cft(g, f):
+    result = np.zeros(len(f), dtype=complex)
+
+    for i, ff in enumerate(f):
+        result[i] = complex_quad(lambda t: g(t)*np.exp(-2j*np.pi*ff*t), -5, 5)
+
+    return result
+
+def complex_quad(g, a, b):
+    t = np.linspace(a, b, 2501)
+    x = g(t)
+    return sp.integrate.simpson(y=x, x=t)
+
+
+def main():
+    g = lambda t: np.sinc(0.5*t/np.pi)
+
+    f_s = 1
+    T_s = 1/f_s
+    t_0 = 1000
+    t = np.arange(-t_0, t_0, T_s)
+    f = np.linspace(-f_s/2, f_s/2, len(t), endpoint=False)
+    omega = 2*np.pi*f
+
+    G = np.fft.fftshift(np.fft.fft(g(t)) * np.exp(-2j*np.pi*f*t_0) /f_s)
+    G_analytic = 2*np.pi*(np.heaviside(omega+0.5, 1) - np.heaviside(omega-0.5, 1))
+
+    plt.plot(f, G_analytic, color="red")
+    plt.scatter(f, G)
+    plt.show()
+    
+
+
+if __name__ == "__main__":
+    main()