# 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 ```

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## 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 eat 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)

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