Signals & Systems-R (FA22)
Assignment # 2 (CLO2)
Due on: Friday, Oct. 28, 2022
Max Marks: 20
Problem 1
The input 𝑥(𝑡) and the impulse response ℎ(𝑡) of an LTI system H are given by following
expressions. Compute and plot the output 𝑦(𝑡) of the system giving all the details.
𝑥(𝑡) = {
-
1, 1 ≤ 𝑡 ≤ 3
;
0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
𝑡 + 2, − 2 ≤ 𝑡 ≤ −1
ℎ(𝑡) = {
0,
𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
Also determine if the system is stable? Causal? Memoryless?
Problem 2
Consider a DT LTI system, 𝐻2 with a unit impulse response ℎ2 [𝑛] = ℎ[𝑛] ∗ ℎ[𝑛 + 1], as
shown below, where ℎ[𝑛] = 𝛿[𝑛] − 𝛿[𝑛 − 1].
(a) Assume that the input to the system, 𝑝[𝑛] is as shown, and 𝑑[𝑛] = 0. Provide a labeled
sketch of 𝑦[𝑛], the output of the system.
(b) For the same input signal as Part (a), now assume that 𝑑[𝑛] = −𝛿[𝑛 + 1]. Provide a labeled
sketch of the output 𝑦[𝑛].
(c) We would like to add an LTI system 𝐻𝑠 whose impulse response, ℎ𝑠 [𝑛] is shown below.
The overall system can be represented as below. Provide a labeled sketch of the overall
output 𝑦𝑠 [𝑛], when 𝑝[𝑛] and 𝑑[𝑛] are exactly the same as in Part (b).
Important Note:
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Assignments should be solved on plain A-4 paper.
Give details of your work to earn maximum score.
Try to solve all problems independently or in groups but avoid copying and turning in other’s solution.
Assignments submitted after the due date will not be accepted.