dr. amit kumar week -5 (13th april...

Dr. Amit Kumar Week -5 (13th – 18th April 2020)

In response to DU's Press release dated 12th March 2020 regarding prevention of pandemic condition arising due to COVID-19, this study material, is prepared for B. Sc. (Hons.) Electronics (IV Sem.) Students on Paper Signals & Systems, at BCAS, DU. Please login to https://amitkumar.moodlecloud.com/ and participate in continuous teaching-learning as per BCAS, DU & UGC directives under National Lockdown period.

Class test will be held on 15th April 2020 at 12 noon @ MOODLE LMS, to attempt it all need to

register on

@ https://amitkumar.moodlecloud.com/login/index.php

Please ensure same.

Now in this study material we will discuss inverse Laplace transforms.

Inverse Laplace Transforms & its Properties

As per definition inverse Laplace transformation i.e. finding f(t) from F(s) is

But this is not that useful as doing this integration is not easy. In fact table given in Ex. 20 of last

week’s study material may be used to find inverse Laplace transformations.

Ex.21 Inverse Laplace Transform Example

Ex.22 Inverse Laplace transformation for some of the basics elementary functions are given

in table below, (remember these are driven from earlier derivations of Laplace

transformations):

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Properties of Laplace transformations:

Ex. 23 Linearity Properties




Ex. 24 First Shifting property

For example,

Ex. 25 Second shifting property

Ex. 26 Change of scale property




Ex. 27 Inverse Laplace transformation for derivative

Ex. 28 Inverse Laplace transform of Integral

Ex. 29 Multiplication by sn




Ex. 30 Division by s

Ex. 31-33 (H.W.)

Ex. 34 (H.W.)




Ex. 35

Inverse Laplace Transformations using Partial Fractions

Having being studied basics for Laplace transformation and inverse Laplace transforms, now we

can discuss, Partial fraction method to find Inverse Laplace transforms.




Ex. 36 let us find inverse Laplace transform using Partial Fraction method

Ex. 37.




Ex. 38.

Ex. 39.




Ex. 40 Prove:

Ex. 41. Prove:

Ex. 42. Find:

Ex. 43. Find:




Ex. 44. Find:

Ex. 45. Prove:

Solving Differential equations using Laplace Transformations




Ex. 46 Let us first solve simple ordinary differential equation with constant coefficients.

Ex. 47




Ex. 48

Ex. 49 (H.W.)

Ex. 50 (H.W.)




Signals & Systems-Experiments

Having completed the experiments on Signals & Systems on SciLAB, all need to submit the

softcopy of files to [email protected] or https://amitkumar.moodlecloud.com/.

LAST DATE: 20-04-2020

Ensure it carries all the experiments we done during contact-hours and lockdown period.

1. Plotting signals Continues time

2. Plotting signals Discrete time

3. Shifting of signals Continues time

4. Shifting of signals Discrete time

5. Convolution of Discrte time signals

6. Verification of properties of convolution

7. Calculating DTFS coefficients of periodic DT signals (magnitude & Phase spectrum

plotting)

8. Calculating inverse DTFS coefficients of periodic DT signals

9. Calculating DTFS coefficients of periodic DT signals (magnitude & Phase spectrum

plotting) Using FFT instruction.

10. Calculating inverse DTFS coefficients of periodic DT signals. Using IFFT instruction.


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dr. amit kumar week -5 (13th april...

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