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Sheet 2

The document contains exercises related to signals and systems, including classification of systems as static, linear, shift invariant, causal, and stable. It also includes tasks for determining causality, computing linear convolution for given sequences, and completing sentences related to system characteristics. The exercises are intended for first-year engineering students at Tanta University in the Computers & Control Department.

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11 views2 pages

Sheet 2

The document contains exercises related to signals and systems, including classification of systems as static, linear, shift invariant, causal, and stable. It also includes tasks for determining causality, computing linear convolution for given sequences, and completing sentences related to system characteristics. The exercises are intended for first-year engineering students at Tanta University in the Computers & Control Department.

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canikissuporfavor
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© © All Rights Reserved
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Tanta University 1st year, Computers & Control Dept.

Faculty of Engineering Signals and Systems

Sheet 2

1. State whether the following system are static, linear, shift invariant, causal, and stable or not.
a. 𝑦(𝑡) = 𝑡 − 𝑥(𝑡 2 − 3)
b. 𝑦(𝑡) = 𝑥(𝑡 2 )
c. 𝑦(𝑡) = (𝑡 + 1)(0.5)𝑥(𝑡)
d. 𝑦(𝑛( = 𝑥(𝑡) cos (𝑥(𝑡 + 1))
e. 𝑦(𝑡) = (2)𝑡−1 𝑥(2𝑡 − 3)
f. 𝑦(𝑛) = 2𝑛 + 𝑥(𝑛2 + 2)
g. 𝑦(𝑛) = (0.5)𝑛+1 𝑥(𝑛)
h. 𝑦(𝑛( = 𝑥(𝑛) cos (𝑤𝑛 + 1)
i. 𝑦(𝑛) = 𝑥(𝑛) + 3𝑢(𝑛 + 1)

2. State whether the following system are causal or non-causal.


a. ℎ(𝑛) = { 1, 2, −1, 1, −0.5}

b. ℎ(𝑛) = {−1, 2, −1, 1, −0.5}

c. ℎ(𝑛) = 𝛿(𝑛) − 𝛿(−𝑛 − 1) − 2 𝛿(𝑛 − 1) + 𝛿(𝑛 − 3) + 𝛿(−𝑛 − 3)

3. Compute the linear convolution , 𝑦(𝑛) = 𝑥 (𝑛) ∗ ℎ(𝑛) , for the following sequences:

a. 𝑥(𝑛) = { 1, 2, −1} and ℎ(𝑛) = 𝑥(𝑛)

b. 𝑥(𝑛) = { 1, 2, 3, 4, 5 } and ℎ(𝑛) = { 1}

1, −1≤𝑛 ≤1
c. 𝑥(𝑛) = ℎ(𝑛) = {
0 , 𝑒𝑙𝑠𝑒𝑤ℎ𝑒𝑟𝑒

Dr. M. Arafa Signals and Systems Course


1 , 𝑛 = −2, 0, 1
d. 𝑥(𝑛) = { 2 , 𝑛 = −1 , and
0 𝑒𝑙𝑠𝑒𝑤ℎ𝑒𝑟𝑒

ℎ(𝑛) = 𝛿(𝑛 + 1) − 𝛿(𝑛 − 1) + 𝛿(𝑛 − 2)

e. 𝑥(𝑛) = {1 , −1 , 0 , 1 , 1} , and ℎ(𝑛) = 2𝑢(𝑛) − 2𝑢(𝑛 − 2)

f. 𝑥(𝑛) = 𝑢(𝑛) , and ℎ(𝑛) = 𝛿(𝑛) + 0.5 𝛿(𝑛 − 1) − 𝛿(𝑛 − 2)

4. Complete the following sentences:

a) If the input and output characteristics of the system change with shift of time, then the

system is called ……….. .

b) The type of system that needs a memory for its operations is called ……….. .

c) If the input output characteristics of the system change with shift of time, then the system

is called .………..

d) If the system output depends upon the future input values, then the system is called

.………..

e) The linear convolution is used to ………..

Dr. M. Arafa Signals and Systems Course

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