 # Homework Assignment: Discrete-time Fourier Transforms 1 Linear co...

## Question

Show transcribed text

## 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.

## Solution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

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...

By purchasing this solution you'll be able to access the following files:
Solution.zip.

# 50% discount

Hours
Minutes
Seconds
\$45.00 \$22.50
for this solution

or FREE if you
register a new account!

PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

### Find A Tutor

View available Electrical Engineering Tutors

Get College Homework Help.

Are you sure you don't want to upload any files?

Fast tutor response requires as much info as possible.