Question
Transcribed Text
Homework Assignment:
Discrete-time Fourier Transforms
1 Linear convolution (10 pts)
Create an animation that demonstrates step-by-step how the output of a convolution is computed. Choose three interesting input and impulse response
signal pairs to produce three different animations, but let the first pair be
x[n] = ∑N
k= N δ[n − kT] and h[n] = a
nu[n] with 0 < a < 1.
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import numpy as npimport matplotlib.pyplot as plt
from scipy import signal
a = 0.9
'''
ANIMATION OF CONVOLUTION:
x[n] = delta function
h[n] = a^n
'''
n = np.arange(-50, 50)
h = np.array([0 for i in range(int(len(n)/2))] + [a**i for i in range(int(len(n)/2))])
convolution = np.zeros(len(n))
for i in range(len(n)):
plt.subplot(3,1,1)
plt.cla()
plt.title("Convolution of Delta Function with a^n, a = " + str(a))
plt.plot(n, h, color="red")
plt.ylabel("h[n]")
plt.subplot(3,1,2)
plt.cla()
x = signal.unit_impulse(100, i)
plt.plot(n, x, color="blue")
plt.ylabel("x[n]")
plt.subplot...
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