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Assignment 2 signal and systems, Assignments of Signals and Systems

Questions get repeated sometimes from previous year papers or similar sort of questions are given.This could be helpful.

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2019/2020

Available from 08/08/2021

meetendra-singh
meetendra-singh 🇮🇳

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EED-201 (Signals and Systems): ASSIGNMENT 2
Submit on / before Oct. 16, 2020.
Solve all the questions.
1. Determine the Fourier series coefficients and the corresponding Fourier series representation
for the continuous time signal below (with time period of 2):
𝑥(𝑡) = 𝑒−𝑡 for 1 < 𝑡 < 1
2. Determine the signal 𝑥(𝑡), having a time period 4 and given the following Fourier series
coefficients (𝑎𝑘):
𝑎𝑘= (−1)𝑘sin𝑘𝜋/8
2𝑘𝜋 , 𝑎0=1
16
3. Determine the Fourier series coefficients and the corresponding Fourier series representation
for the discrete time signal below (with period 12):
𝑥[𝑛] = 1 sin 𝜋𝑛
4 for0 𝑛 11
4. Determine the signal 𝑥[𝑛], having a period 8 and given Fourier series coefficients (𝑎𝑘) in the
figure below:
5. Consider a discrete-time LTI system with the following impulse response:
ℎ[𝑛] = (1
2)|𝑛|
Find the Fourier series representation of the output 𝑦[𝑛] for each of the following inputs 𝑥[𝑛]:
1) 𝑥[𝑛] =
𝑘=−∞ 𝛿[𝑛 4𝑘]
2) 𝑥[𝑛] is periodic signal with period 6 and,
𝑥[𝑛] = {1, 𝑛 = 0, ±1
0, 𝑛 = ±2,±3

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EED-201 (Signals and Systems): ASSIGNMENT 2 Submit on / before Oct. 16, 2020. Solve all the questions.

  1. Determine the Fourier series coefficients and the corresponding Fourier series representation for the continuous time signal below (with time period of 2): 𝑥(𝑡) = 𝑒−𝑡^ for − 1 < 𝑡 < 1
  2. Determine the signal 𝑥(𝑡), having a time period 4 and given the following Fourier series coefficients (𝑎𝑘):

𝑘sin𝑘𝜋/ 8

1 16

  1. Determine the Fourier series coefficients and the corresponding Fourier series representation for the discrete time signal below (with period 12): 𝑥[𝑛] = 1 − sin 𝜋𝑛 4 for0 ≤ 𝑛 ≤ 11
  2. Determine the signal 𝑥[𝑛], having a period 8 and given Fourier series coefficients (𝑎𝑘) in the figure below:
  3. Consider a discrete-time LTI system with the following impulse response: ℎ[𝑛] = ( 1 2

|𝑛| Find the Fourier series representation of the output 𝑦[𝑛] for each of the following inputs 𝑥[𝑛]:

  1. 𝑥[𝑛] = ∑∞ 𝑘=−∞ 𝛿[𝑛 − 4 𝑘]
  2. 𝑥[𝑛] is periodic signal with period 6 and, 𝑥[𝑛] = {