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
