Getting started guide

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

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+% Lab 1
+% Question 1 on aliasing
+
+fs=100;						% Sampling frequency [Hz]
+ts=1/fs;					% Sampling period [s]
+
+n=0:1:9;					% Sample indicies
+x20(n+1)=cos(2*pi*20*n*ts); % x[n] with f = 20 [Hz]
+x80(n+1)=cos(2*pi*80*n*ts); % x[n] with f = 80 [Hz]
+
+subplot(211)				% Start top sub plot
+stem(n,x20,'linewidth',2)	% Plot samples of x[n] with f = 20[Hz] for all n
+subplot(212)				% Start bottom sub plot
+stem(n,x80,'linewidth',2)	% Plot samples of x[n] with f = 80[Hz] for all n
+xlabel('f = 20 and 80 Hz'); % Label the x axis
+

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

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+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]
+
+    n = np.arange(10)           # Samples starting at zero, up to, but not including 10
+    t = n*T_s                   # Convert from sample domain to time domain
+
+    x_20 = np.cos(2*np.pi*20*t) # Cosine signal x[n] with f = 20[Hz]
+    x_80 = np.cos(2*np.pi*80*t) # Cosine signal x[n] with f = 80[Hz]
+
+    plt.subplot(211)            # Begin top subplot
+    plt.stem(n, x_20)           # Plot samples of x (x_20) over sample indicies (n)
+    plt.subplot(212)            # Begin bottom subplot
+    plt.stem(n, x_80)           # Plot samples of x (x_80) over sample indicies (n)
+
+    plt.show()                  # Show the plot
+
+if __name__ == "__main__":
+    main()

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

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+syms W
+for k=1:24;
+E(k)=single(int((sin(0.5*W)/(0.5*W))^2 ,W,0,k*pi)/pi);
+end
+stem(E,'linewidth',2); 
+hold on
+EE=0.9900*ones(1,24); 
+plot(EE,'r','linewidth',2)
+set(gca,'XTick',0:5:25)
+set(gca,'XTickLabel',{'0','5\pi','10\pi','15\pi','20\pi','25\pi'})
+xlabel('Angular frequency')
+ylabel('Signal Energy')
+axis([0 25 0 1.1])

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

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+syms t
+a=simplify(fourier(sin(0.5*t)/(0.5*t)))

8th-Semester-Spring-2025/clinic-consultant/labs/lab-1/lab1q4.m

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+% Lab 1
+% Question 4 
+
+fs=4;
+ts=1/fs;
+
+n=0:1:99;
+x(n+1)=cos(2*pi*n*ts/5)+sin(4*pi*n*ts/7)+cos(16*pi*n*ts/9);
+
+stem(n,x,'linewidth',2);
+xlabel('n')
+ylabel('x(n)')

8th-Semester-Spring-2025/clinic-consultant/labs/lab-1/lab1q5.m

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+syms t
+f=exp(-t*4)*heaviside(t);
+ff=fourier(f);

8th-Semester-Spring-2025/clinic-consultant/labs/lab-1/lab1q6.m

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+syms a b t
+assume(a > 0)
+f = exp(-a*abs(t));
+ff = fourier(f);
+
+assume(b > 0)
+g = f*cos(b*t);
+gg = simplify(fourier(g));
+