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Analog Communications for GATE and other Exams
Rating: 4.5 out of 5(1 rating)
6 students

Analog Communications for GATE and other Exams

Completeness of each topic of Analog Communications with utmost clarity
Created byDURGASOFT DURGA
Last updated 2/2022
English
English [Auto],

What you'll learn

  • Students can get complete in-depth knowledge of Communication & System
  • Can get the knowledge of Communication & System
  • Can get the knowledge of AM power Calculations
  • Can get the knowledge of Square law Modulator - AM Generation

Course content

2 sections • 63 lectures • 10h 33m total length

  • Introduction to Fourier Transforms & Dirichlet s conditions9:42

    Explore how Fourier transforms link time signals to the frequency domain and their discrete versions for digital signal processing, and study Dirichlet conditions: absolute integrability, finite discontinuities, and finite extrema.

  • Fourier Transform of Unit Impulse function and One sided Exponential13:53

    Explore the Fourier transform of the unit impulse and one-sided exponential signals, applying shifting properties, spectrum magnitude and phase, and practical spectrum visualization.

  • Fourier Transform of Two sided Exponential.8:40

    Explore the Fourier transform of a two-sided exponential signal, derive a real spectrum with no imaginary part, and illustrate its magnitude spectrum and behavior across omega.

  • Fourier Transform of Signum Function7:46

    derive the Fourier transform of the signum function by regularizing with a decaying factor, showing the transform equals minus two omega divided by omega squared in the limit.

  • Fourier Transform of Unit Step function & Sinusoidal Functions.6:22

    explain the Fourier transform of the unit step function and sinusoidal functions within analog communications, using complex exponentials and two approaches.

  • Fourier Transform of Rectangular & Sinc & Fampling Functions.15:01

    Explore the Fourier transform of the rectangular function, its relation to sinc, and how sampling functions arise via the duality property in frequency analysis.

  • Fourier Transform of Triangular Function10:11

    Analyze the Fourier transform of a triangular and trapezoidal function by using differentiation properties, delta and step functions, and ramp representations, deriving a sinc-squared form through delta-based expansion.

  • Fourier Transform of Trapezoidal Signal5:51

    Explore the Fourier transform of a trapezoidal signal by decomposing it into ramp and step functions, deriving the second derivative as delta functions, and applying differentiation properties.

  • Linearity property of Fourier Transform5:07
  • Time scaling property of Fourier Transform5:34

    Explore the time scaling property of the Fourier transform and how time-domain scaling by a constant affects the spectrum and magnitude symmetry.

  • Time shifting property of Fourier Transform4:41

    Derives the time shifting property of the Fourier transform, showing that shifting a signal by d multiplies its Fourier transform by e^{-j ω d} with X(ω).

  • Frequency shifting property of Fourier Transform4:07

    Explain the frequency shifting property of the Fourier transform: a frequency shift corresponds to multiplying the time-domain signal by an exponential with a minus sign. Contrast with time shifting.

  • Differentiation in Time property of Fourier Transform5:29

    Explain how differentiating a time-domain signal corresponds to multiplying its Fourier transform by omega, and derive the differentiation property from the transform definition.

  • Integration in Time domain Property of Fourier Transform6:20

    The lecture presents the time-domain integration property of the Fourier transform, proves it by interchanging integrals, and identifies the result as the Fourier transform of the signal.

  • Differentiation in Frequency domain Property of Fourier Transform5:01

    Explain and prove the differentiation in the frequency domain property of the Fourier transform, including how taking derivatives with respect to omega affects the transform and its inverse.

  • Conjugation Property of Fourier Transform4:22

    Explore the conjugation property of the Fourier transform, showing how the complex conjugate of the transform relates to the transform at negative frequencies and proving the symmetry.

  • Duality Property of Fourier Transform3:46

    Explore the duality property of the Fourier transform, linking time-domain signals to their frequency-domain representations via reflection, and see how this property is proven from the standard transform.

  • Modulation Property of Fourier Transform5:39

    Explore the modulation property of the Fourier transform in spectral analysis for analog communications. Multiplying a signal by a sinusoid shifts its spectrum by the carrier frequency.

  • Area Under time and Frequency Domain Signals.8:38

    Explore how to determine the area under time-domain and frequency-domain signals using the area property of the Fourier transform, including cross-domain equivalence and rectangle functions.

  • Time Convolution Property of Fourier Transform7:56

    Explore the time and frequency domain convolution properties and their use in system analysis, showing that the Fourier transform of a convolution equals the product of the individual transforms.

  • Frequency Convolution Property of Fourier Transform8:54

    Show that the Fourier transform of the product x1(t) x2(t) equals the convolution of X1(ω) and X2(ω) in the frequency domain, illustrating the frequency-domain convolution property.

  • Parseval's relation8:02
  • Fourier Transform of Periodic Signal6:39
  • GATE Previous Problems with Solutions Set - 111:40

    Analyze the time-domain and frequency-domain behavior of a system using impulse response, convolution, and Fourier transforms; apply time shifting and exponential properties to determine the output for GATE problems.

  • GATE Previous Problems with Solutions Set - 217:09

    Learn to compute signal energy via Fourier transform, shifting and scaling properties, and time-domain and frequency-domain relations using rectangle functions and sampling.

  • Convolution & Examples19:00

    Explore convolution and deconvolution fundamentals in analog communications, using unit step and unit impulse, exploring commutative and distributive properties and impulse-response of LTI systems.

  • Convolution Graphical procedure exponential with unit step6:22

    Perform graphical convolution of an exponentially decaying signal with a left-shifted unit step, applying time-index shifts and interval constraints. Arrive at y(t) = (1/3)[1 − e^{-3(t+3)}] for t > −3.

  • Convolution Graphical procedure two rectangular signals10:32

    learn to perform convolution of two rectangular signals with a graphical procedure, applying shift, reflection, and product integration to obtain a trapezoidal (or triangular) output.

  • Triangular and rectangular convolution9:31

    Compute the convolution of a triangular function with a rectangular function using graphical and piecewise integration to reveal the nonzero result across intervals and the resulting convolved shape.

Requirements

  • Should have knowledge of trigonometry
  • Should have knowledge of differentiation and integration
  • Should have knoweldge of algebraic equations

Description

Fourier Transform

============

1. Introduction to Fourier Transforms & Dirichlet s conditions                          

2. Fourier Transform of Unit Impulse function and One sided Exponential.   

3. Fourier Transform of Two sided Exponential.

4. Fourier Transform of Signum Function

5. Fourier Transform of Unit Step function & Sinusoidal Functions.

6. Fourier Transform of Rectangular & Sinc & Fampling Functions.

7. Fourier Transform of Triangular Function.

8. Fourier Transform of Trapezoidal Signal.

9. Linearity property of Fourier Transform   

10. Time scaling property of Fourier Transform

11. Time shifting property of Fourier Transform

12. Frequency shifting property of Fourier Transform

13. Differentiation in Time property of Fourier Transform

14. Integration in Time domain Property of Fourier Transform

15. Differentiation in Frequency domain Property of Fourier Transform

16. Conjugation Property of Fourier Transform

17. Duality Property of Fourier Transform

18. Modulation Property of Fourier Transform

19. Area Under time and Frequency Domain Signals.

20. Time Convolution Property of Fourier Transform

21. Frequency Convolution Property of Fourier Transform

22. Parseval's relation

23. Fourier Transform of Periodic Signal

24. GATE Previous Problems with Solutions Set - 1

25. GATE Previous Problems with Solutions Set - 2


Communication & System

==================

1.Time Domain Analysis AM

2.Single tone AM

3.Power Calculations AM

4.Multi tone AM

5.limitations of AM

6.Square law Modulator - AM Generation

7.Switching Modulator - AM Generation

8.Coherent Detector - AM Detection

9.Square law detector-AM Detection

10.Example problems on AM

11.GATE problems on AM Set - 1 

12.GATE problems on AM Set - 2

13.GATE problems on AM Set - 3

14.DSB introduction

15.Balanced Modulator-DSB generation

16.Ring Modulator - DSB Generation

17.Coherent detector - DSB Detection

18.Costas Loop/Receiver - DSB Detection

19.DSB example problem

20.GATE - Problems on DSB Set - 1

21.GATE - Problems on DSB Set - 2

22.SSB Introduction

23.SSB Time domain representation

24.SSB Generation-Frequency and Phase Descrimination Methods

25.SSB Detection - Coherent Detector

26.Single tone FM

27.Narrow Band FM(NBFM)

28.Wide Band FM(WBFM)

29.Carson's rule for FM bandwidth

30. Example Problems Set - 1 FM

31. Example Problems Set - 2 FM

32.GATE FM Problems

33.Super Heterodyne Receiver

34.Super heterodyne Receiver Example Problems



Who this course is for:

  • Engineering students appearing for University and Competitive Examinations.

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