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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 np
import 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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