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Assignment 4 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.

Typology: Assignments

2019/2020

Available from 08/08/2021

meetendra-singh
meetendra-singh 🇮🇳

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EED-201: Assignment 4 (Laplace transform)
1. Find the inverse laplace transform of:
i) 𝑋(s) = s2+2s+5
(s+3)(s+5)2 , Re(s) > -3 ii) 𝑋(s) = 2𝑠+1
s+2 , Re(s) > -2
iii) 𝑋(s) = 𝑠3+2s2+6
𝑠2+3𝑠 , Re(s) > 0
2. Find the laplace transform of the following x(t):
i) x(t) = cos(𝜔0𝑡 + 𝜙) 𝑢(𝑡)
ii) x(t)= 𝑒𝑎𝑡 𝑢(𝑡) 𝑒𝑎𝑡𝑢(−𝑡)
iii) x(t)= 𝑠𝑔𝑛(𝑡)
3. The step response of a continuous-time LTI system is given by 1 𝑒−𝑡𝑢(𝑡). For a certain
unknown input x(t), the output y(t) is observed to be (2 3𝑒−𝑡 + 𝑒−3𝑡)𝑢(𝑡). Find the input
x(t).
4. Consider two right-sided signals x(t) and y(t) related through the differential
equations: 𝑑𝑥(t)
dt = −2𝑦(𝑡)+ 𝛿(𝑡)
and 𝑑𝑦(t)
dt = 2𝑥(𝑡)
Determine X(s) and Y(s) along with their regions of convergence.
5. A causal LTI system S has the block diagram representation shown in the figure below.
Determine a differential equation relating the input x(t) to the output y(t) of this system.
6. The system function of a causal LTI system is given by:
𝐻(𝑠)=𝑠+1
𝑠2+2𝑠+2
Determine and sketch the response y(t) when the input is: 𝑥(𝑡)= 𝑒|𝑡|, −∞ < 𝑡 < ∞.

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EED-201: Assignment 4 (Laplace transform)

  1. Find the inverse laplace transform of:

i) 𝑋(s) =

s

2

+2s+ 5

(s+ 3 )(s+ 5 )

2

, Re(s) > - 3 ii) 𝑋(s) =

2 𝑠+ 1

s+ 2

, Re(s) > - 2

iii) 𝑋(s) =

𝑠

3

  • 2 s

2

  • 6

𝑠

2

  • 3 𝑠

, Re(s) > 0

  1. Find the laplace transform of the following x(t):

i) x(t) = cos(𝜔

0

ii) x

t

−𝑎𝑡

𝑎𝑡

iii) x(t) = 𝑠𝑔𝑛(𝑡)

  1. The step response of a continuous-time LTI system is given by 1 − 𝑒

−𝑡

𝑢(𝑡). For a certain

unknown input x(t), the output y(t) is observed to be ( 2 − 3 𝑒

−𝑡

− 3 𝑡

)𝑢(𝑡). Find the input

x(t).

  1. Consider two right-sided signals x(t) and y(t) related through the differential

equations:

𝑑𝑥(t)

dt

and

𝑑𝑦

( t

)

dt

Determine X(s) and Y(s) along with their regions of convergence.

  1. A causal LTI system S has the block diagram representation shown in the figure below.

Determine a differential equation relating the input x(t) to the output y(t) of this system.

  1. The system function of a causal LTI system is given by:

𝐻

( 𝑠

)

𝑠+ 1

𝑠

2

  • 2 𝑠+ 2

Determine and sketch the response y(t) when the input is: 𝑥

( 𝑡

) = 𝑒

−|𝑡|

, −∞ < 𝑡 < ∞.