EED-201: Assignment 4 (Laplace transform)
1. Find the inverse laplace transform of:
i) ๐(s) = s2+2s+5
(s+3)(s+5)2 , Re(s) > -3 ii) ๐(s) = 2๐ +1
s+2 , Re(s) > -2
iii) ๐(s) = ๐ 3+2s2+6
๐ 2+3๐ , Re(s) > 0
2. Find the laplace transform of the following x(t):
i) x(t) = cos(๐0๐ก + ๐) ๐ข(๐ก)
ii) x(t)= ๐โ๐๐ก ๐ข(๐ก)โ ๐๐๐ก๐ข(โ๐ก)
iii) x(t)= ๐ ๐๐(๐ก)
3. The step response of a continuous-time LTI system is given by 1โ ๐โ๐ก๐ข(๐ก). For a certain
unknown input x(t), the output y(t) is observed to be (2 โ 3๐โ๐ก + ๐โ3๐ก)๐ข(๐ก). Find the input
x(t).
4. Consider two right-sided signals x(t) and y(t) related through the differential
equations: ๐๐ฅ(t)
dt = โ2๐ฆ(๐ก)+ ๐ฟ(๐ก)
and ๐๐ฆ(t)
dt = 2๐ฅ(๐ก)
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:
๐ป(๐ )=๐ +1
๐ 2+2๐ +2
Determine and sketch the response y(t) when the input is: ๐ฅ(๐ก)= ๐โ|๐ก|, โโ < ๐ก < โ.
