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
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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):
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.
Properties of Laplace transformations:
Ex. 23 Linearity Properties
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.
Ex. 24 First Shifting property
For example,
Ex. 25 Second shifting property
Ex. 26 Change of scale property
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.
Ex. 27 Inverse Laplace transformation for derivative
Ex. 28 Inverse Laplace transform of Integral
Ex. 29 Multiplication by sn
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.
Ex. 30 Division by s
Ex. 31-33 (H.W.)
Ex. 34 (H.W.)
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.
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.
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.
Ex. 36 let us find inverse Laplace transform using Partial Fraction method
Ex. 37.
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.
Ex. 38.
Ex. 39.
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.
Ex. 40 Prove:
Ex. 41. Prove:
Ex. 42. Find:
Ex. 43. Find:
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.
Ex. 44. Find:
Ex. 45. Prove:
Solving Differential equations using Laplace Transformations
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.
Ex. 46 Let us first solve simple ordinary differential equation with constant coefficients.
Ex. 47
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.
Ex. 48
Ex. 49 (H.W.)
Ex. 50 (H.W.)
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.
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.