Consultant lab 4

8th-Semester-Spring-2025/clinic-consultant/labs/lab-4/lab4q1.m

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+% Set up x[n] for N=8
+N = 8;
+n = 0 : N-1
+x = (-1.0).^n;
+
+% 8-point DFT for N=8
+dft8 = fft(x, 8);
+stem(abs(dft8));
+
+% 9-point DTF for N=8
+figure(2);
+dft9 = fft(x, 9);
+stem(abs(dft9));

8th-Semester-Spring-2025/clinic-consultant/labs/lab-4/lab4q1.py

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+import numpy as np
+import matplotlib.pyplot as plt
+
+
+# Set up N=8
+N = 8
+n = np.arange(N)
+x = (-1.0)**n
+
+# 8-point DFT, N=8
+DFT_8_point = np.fft.fft(x, 8)
+plt.stem(abs(DFT_8_point))
+plt.savefig("N8_point_dft.png")
+plt.show()
+
+# 9-point DFT, N=8
+DFT_9_point = np.fft.fft(x, 9)
+plt.stem(abs(DFT_9_point))
+plt.savefig("Q9_point_dft.png")
+plt.show()
+
+# 9-point DFT, N=9
+N = 9
+n = np.arange(N)
+x = (-1.0)**n
+DFT_9_point = np.fft.fft(x, 9)
+plt.stem(abs(DFT_9_point))
+plt.savefig("N9_point_dft.png")
+plt.show()

8th-Semester-Spring-2025/clinic-consultant/labs/lab-4/lab4q2.m

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+syms n a b
+
+f1 = a^n;
+ztrans(f1);
+
+f2 = (n+1) * a^n * heaviside(n);
+ztrans(f2);
+
+f3 = a^n * cos(b*n) heaviside(n);
+ztrans(f3);

8th-Semester-Spring-2025/clinic-consultant/labs/lab-4/lab4q3.m

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+syms z
+
+f1 = iztrans(z / (z+0.5))
+f2 = iztrans(z^2 / (z-0.8)^2 )
+f3 = simplify(iztrans(z / ( (z+0.3)*(z+0.6)^2 ))