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Consultant evaluation and lab 3

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This commit is contained in:
Aidan Sharpe
2025-03-10 15:24:54 -04:00
parent 0ee36aae38
commit 75ff89644d
24 changed files with 8610 additions and 1 deletions
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49
8th-Semester-Spring-2025/clinic-consultant/labs/lab-3/lab3q1.m Normal file
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% value of a
a=0.9;
% signal x(n)
for n=0:200
x(n+1) = a^n;
end
figure(1)
n=0:1:200;
stem(n,x)
xlabel('n');
ylabel('x(n)');
% question part (e)
n=1;
d=[1 -a];
[h1,w]=freqz(n,d,256);
h1mag=abs(h1);
figure(2)
plot(w,h1mag,'b','linewidth',2)
xlabel('Frequency');
ylabel('Magnitude Response');
% partial dtft for k =3
[h2,w]=freqz(x(1:4),1,256);
h2mag=abs(h2);
hold
plot(w,h2mag,'r','linewidth',2)
% partial dtft for k =10
[h3,w]=freqz(x(1:11),1,256);
h3mag=abs(h3);
plot(w,h3mag,'m','linewidth',2)
% partial dtft for k =20
[h4,w]=freqz(x(1:21),1,256);
h4mag=abs(h4);
plot(w,h4mag,'k','linewidth',2)
% supremum coefficients of the error
for k=1:200
[hk,w]=freqz(x(1:k+1),1,256);
ek=abs(h1-hk);
coeff(k)=max(ek);
end
figure(3)
k=1:1:200;
stem(k,coeff)

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8th-Semester-Spring-2025/clinic-consultant/labs/lab-3/lab3q1.py Normal file
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import numpy as np
import scipy as sp
import matplotlib.pyplot as plt
DATA_POINTS = 200
def u(n):
return np.heaviside(n, 1)
def main():
a = 0.9
n = np.arange(DATA_POINTS)
x = a**n * u(n)
# Plot samples of x[n]
plt.figure()
plt.stem(n, x)
plt.xlabel("n")
plt.ylabel(r"$x[n]$")
# Plot the analytical DTFT
numerator = 1
denominator = [1, -a]
omega, h_0 = sp.signal.freqz(numerator, denominator, 256)
plt.figure()
plt.plot(omega, np.abs(h_0), label="Analytical DTFT")
plt.xlabel("Frequency")
plt.ylabel("Magnitude Response")
# Plot the truncated DTFT for K = 3, 10, 20
for K in (3, 10, 20):
omega, h = sp.signal.freqz(x[:K], 1, 256)
plt.plot(omega, np.abs(h), label=f"Truncated DTFT ($K = {K}$)")
plt.legend()
# Calculate the maximum error between the truncated DTFT
# and the analytical DTFT for values of K from 1 to 200
k = np.arange(DATA_POINTS)
coeffs = np.zeros_like(k, dtype=np.float32)
for i_k in k:
omega, h_k = sp.signal.freqz(x[:i_k], 1, 256)
err_k = np.abs(h_0 - h_k)
coeffs[i_k] = np.max(err_k)
# Plot the maximum error previously calculated
plt.figure()
plt.stem(k, coeffs)
plt.xlabel("k")
plt.ylabel("Supremum coefficients of the error")
plt.show()
if __name__ == "__main__":
main()

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8th-Semester-Spring-2025/clinic-consultant/labs/lab-3/lab3q2.m Normal file
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% value of a
a=0.9;
% signal x(n)
for n=0:200
x(n+1) = n*(a^n);
end
figure(1)
n=0:1:200;
stem(n,x)
xlabel('n');
ylabel('x(n)');
% question part (e)
n=[0 a];
d=[1 -2*a a*a];
[h1,w]=freqz(n,d,256);
h1mag=abs(h1);
figure(2)
plot(w,h1mag,'b','linewidth',2)
xlabel('Frequency');
ylabel('Magnitude Response');
% partial dtft for k =3
[h2,w]=freqz(x(1:4),1,256);
h2mag=abs(h2);
hold
plot(w,h2mag,'r','linewidth',2)
% partial dtft for k =10
[h3,w]=freqz(x(1:11),1,256);
h3mag=abs(h3);
plot(w,h3mag,'m','linewidth',2)
% partial dtft for k =20
[h4,w]=freqz(x(1:21),1,256);
h4mag=abs(h4);
plot(w,h4mag,'g','linewidth',2)
% partial dtft for k =40
[h5,w]=freqz(x(1:41),1,256);
h5mag=abs(h5);
plot(w,h5mag,'k','linewidth',2)
% supremum coefficients of the error
for k=1:200
[hk,w]=freqz(x(1:k+1),1,256);
ek=abs(h1-hk);
coeff(k)=max(ek);
end
figure(3)
k=1:1:200;
stem(k,coeff)

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8th-Semester-Spring-2025/clinic-consultant/labs/lab-3/lab3q2.py Normal file
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import numpy as np
import scipy as sp
import matplotlib.pyplot as plt
DATA_POINTS = 200
def u(n):
return np.heaviside(n, 1)
def main():
a = 0.9
n = np.arange(DATA_POINTS)
x = n*(a**n)*u(n)
# Plot samples of x[n]
plt.figure()
plt.stem(n, x)
plt.xlabel("n")
plt.ylabel(r"$x[n]$")
# Plot the analytical DTFT
numerator = [0, a]
denominator = [1, -2*a, a**2]
omega, h_0 = sp.signal.freqz(numerator, denominator, 256)
plt.figure()
plt.plot(omega, np.abs(h_0), label="Analytical DTFT")
plt.xlabel("Frequency")
plt.ylabel("Magnitude Response")
# Plot the truncated DTFT for K = 3, 10, 20
for K in (3, 10, 20):
omega, h = sp.signal.freqz(x[:K], 1, 256)
plt.plot(omega, np.abs(h), label=f"Truncated DTFT ($K = {K}$)")
plt.legend()
# Calculate the maximum error between the truncated DTFT
# and the analytical DTFT for values of K from 1 to 200
k = np.arange(DATA_POINTS)
coeffs = np.zeros_like(k, dtype=np.float32)
for i_k in k:
omega, h_k = sp.signal.freqz(x[:i_k], 1, 256)
err_k = np.abs(h_0 - h_k)
coeffs[i_k] = np.max(err_k)
# Plot the maximum error previously calculated
plt.figure()
plt.stem(k, coeffs)
plt.xlabel("k")
plt.ylabel("Supremum coefficients of the error")
plt.show()
if __name__ == "__main__":
main()

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8th-Semester-Spring-2025/clinic-consultant/labs/lab-3/lab3q3.m Normal file
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% value of a
wc=0.4*pi;
% signal x(n)
for n=-50:50
if (n == 0)
x(n+51) = wc/pi;
else
x(n+51) = sin(wc*n)/(pi*n);
end
end
figure(1)
n=-50:1:50;
stem(n,x)
xlabel('n')
ylabel('x(n)')
% Ideal lpf
n=0;
for w=0:0.05*pi:pi;
n=n+1;
wfreq(n)=w;
if (w <= wc)
hlpf(n)=1;
else
hlpf(n)=0;
end
end
figure(2)
plot(wfreq,hlpf,'b','linewidth',2)
xlabel('Frequency')
ylabel('DTFT of Ideal Lowpass Filter')
% partial dtft for k =10
k=10;
[h2]=freqz(x(51-k:51+k),1,wfreq);
h2mag=abs(h2);
hold
plot(wfreq,h2mag,'r','linewidth',2)
% partial dtft for k =20
k=20;
[h3]=freqz(x(51-k:51+k),1,wfreq);
h3mag=abs(h3);
plot(wfreq,h3mag,'m','linewidth',2)
% partial dtft for k =30
k=30;
[h4]=freqz(x(51-k:51+k),1,wfreq);
h4mag=abs(h4);
plot(wfreq,h4mag,'k','linewidth',2)

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8th-Semester-Spring-2025/clinic-consultant/labs/lab-3/lab3q5.m Normal file
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for n=0:99
y1(n+1) = (1 - (0.95)^(n+1))/0.05;
y2(n+1) = n + 1;
end
figure(1)
n=0:1:99;
stem(n,y1)
xlabel('n')
ylabel('y(n)')
figure(2)
n=0:1:99;
stem(n,y2)
xlabel('n')
ylabel('y(n)')