UNIT 03 : LAPLACE TRANSFORM ANALYSIS | Basic Signal and Systems -AKTU

We are examining the “Electrical and Electronics Engineering” unit 03, “Laplace Transform Analysis,” | “Basic Signal and Systems assignment from AKTU. I hope this article is useful to you as you prepare for your AKTU exams.

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Important Questions For Basic Signals and Systems : 
*Unit-01     *Unit-02    
*Unit-03    *Unit-04 
*Unit-05    *Short-Q/Ans
*Question-Paper with solution 21-22 

Q1. Calculate the Laplace transform for the function F(t) = e^-at sin hbt.

Ans. 

Q2. Find the Laplace transform of signal u(t).  

Ans. 

Q3. What are the different properties of laplace transform ?  

Ans. 1. Linearity: Considering two signals x₁(t) and x₂(t) with Laplace transforms X₁(s) and X₂(s) respectively.   

2. Time shifting: 

If the x(t) signal is delayed in time by t₀ unit then its Laplace transform is multiplied by e^-sto factor. 

3. Frequency shifting: If there is any shift in X(s) by a unit, it will cause a multiplication factor e^at in signal x(t).  

4. Differentiation theorem: 

5. Differentiation by s: In the time-domain, multiplying by t corresponds to differentiation in the complex frequency-domain.  

7. Scaling property: This theorem states that, 

Q4. If the laplace transform of x(t) is (s + 2)/(s² + 4s + 5), determine the laplace transform of y(t) = x(2t – 1) u(2t 1). 

Ans. 1. The Laplace transform of x(t) u(t) is

2. Applying time shifting property. 

3. Now, applying time scaling property. 

4 Hence, the Laplace transform of y(t) = x(2t – 1) u (2t – 1) is, 

Q5. A signal has Laplace transform X(s)

Find the Laplace transform Y(s) of the following signals 

i. y(t) = tx(t)

ii. y(t)=e^-tx(t) 

Ans. 

Q6. Calculate the inverse Laplace transform of right-sided sequences with the following transfer functions:

Ans. 

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