Mô tả

Chapter - 1: Signals

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

1.Deterministic and random signals

2.Analog and Digital Signals

3.Unit impulse Function - Elementary Signals

4.Unit step Function

5.Unit Ramp and Parabolic & Singularity Functions

6. Exponential Functions - Elementary Signals

7. Signum Function - Elementary Signals

8. Rectangular Function - Elementary Signals

9. Triangular Function - Elementary Signals

10. Sinusoidal Functions - Elementary Signals

11. Sinc & Sampling Functions - Elementary Signals

12. Periodic & Non Periodic Signals- Classification

13.Even and Odd Signals

14.Causal and Non Causal Signals

16.Rectangular Function E & P

17.Unit step Function E & P

18.Unit Ramp Function E & P

19.Power of Sinusoidal Signal

20.Effect of shifting and Scaling on E & P

21.Observation Points on E & P

22.Operations on Independent Variable of Signal

23. GATE Previous Problems with Solutions Set - 1

24. GATE Previous Problems with Solutions Set - 2


Chapter - 2: Systems

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

15. 1. Systems Classification - Linear & Nonlinear Systems

16. 2. Systems Classification - Time Variant & time Invariant Systems

17. 3. Static & Dynamic & Causal & Non Causal Systems

18. 4. Examples

19. 5. Stable & Unstable Systems

20. 6. Examples

21  7. Invertible & Non Invertible Systems

23. 9. GATE Previous Problems with Solutions Set - 1

24. 10.GATE Previous Problems with Solutions Set - 2

25. 11.GATE Previous Problems with Solutions Set - 3


Chapter - 3: Fourier Series

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

1. Fourier Series Introduction

2.Orthogonality in Vectors

3.Orthogonality in Signals

4.Orthogonal Signal Space & Signal Approximation

5.Mean Square Error and Complete Set

6.Orthonormal Set

7.Complete Set Example - 1

8.Complete Set Example - 2

9.Orthogonality in Complex Functions

10.Full Wave Rectified signal EFS

11.Dirichlet's Conditions for Fourier Series

12.TFS and EFS Expansion Example

13.Symmetric Conditions

14.Check the Symmetry Conditions for Examples

15 GATE Previous Problems with Solutions Set - 1

16.GATE Previous Problems with Solutions Set - 2 

17.Exponentials periodic signal TFS & EFS

18.Triangular Periodic Signal TFS & EFS

19.Frequency Spectrum


Chapter - 4: 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


Chapter - 5: Laplace Transform

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

1. Laplace Transform of impulse function with ROC

2. LT of unit step Function with ROC

3. LT of left side unit step Function with ROC

4. LT of Exponential Functions with ROC

5. LT of Complex Exponentials & cos and sin Functions with ROC

6. LT and ROC of both side Exponentials

7. LT and ROC of damped sin Function

8. LT and ROC of Damped cos Function

9. LT and ROC of Hyperbolic sin and cos Functions

10. Linearity Property of LT

11. Time shifting Property of LT

12. Frequency shifting Property of LT

13. Time scaling and Time Reversal Property of LT

14. Time Differentiation Property of LT

15. Differentiation in S-domain Property of LT

16. Conjugation property of LT

17. Initial and Final value Theorems of LT

18. Convolution Property of LT

19. GATE Previous Problems with Solutions Set - 1

20. Laplace Transform Example Set - 1

21. Laplace Transform Example Set - 2


Chapter - 6: Z-Transform

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

1. Z-Transform and ROC of unit impulse and step Functions

2. ZT and ROC of u(-n) and -u(-n-1)

3. ZT and ROC of exponentials a^nu(n) and -a^nu(-n-1)

4. ZT and ROC of complex exponentials and coswn.u(n)

5. ZT and ROC of sinwn.u(n)

6. ZT Properties - Linearity

7. ZT Properties - Time shifting

8. ZT properties - Multiplication with exponential

9. ZT Properties - Time Reversal

10. ZT Properties - Time Expansion

11. ZT Properties - Differentiation in Z-Domain

12. ZT Properties - Conjugation

13. ZT Properties - Convolution

14. ZT Properties - Initial value Theorem

15. ZT Properties - Final value Theorem

16. GATE Previous Problems with Solutions Set - 1

17. GATE Previous Problems with Solutions Set - 2

18. GATE Previous Problems with Solutions Set - 3


Chapter - 7: Discrete Fourier Transform

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

1. DTFT(Discrete Time Fourier Transform)

2. DTFT of Impulse & Unit step Functions

3. DTFT of DT Exponential Sequence

4. DFT-Discrete Fourier Transform

5. DFT example

6. GATE Previous Problems with Solutions Set - 1

7. GATE Previous Problems with Solutions Set - 2


Chapter - 8: Sampling Theorem

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

33. 1. Sampling Theorem Definition.

34. 2. Nyquist Condition - NR Calcutions

35. 3. Time Domain & Frequency Domain Analysis(spectral)

36. 4. GATE Previous Problems with Solutions Set - 1


Chapter - 9: Signal Transmission Through LTI System

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

1.Distortionless transmission system and frequency respons

2.Impulse Response of Distortionless transmission system

3.Filter Characteristics of LTI Systems

4.Signal Bandwidth vs System Bandwidth.


Chapter - 10: Convolution & Correlation

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

1.Convolution & Examples

2.Convolution Graphical procedure exponential with unit step

3.Convolution Graphical procedure two rectangular signals

4.Triangular and rectangular convolution

Bạn sẽ học được gì

Students can get complete in-depth knowledge of Signals & Systems

can get the knowledge of fourier series and fourier transforms

can get the knowledge of laplace transforms and z-transforms

can get the knowledge of sampling theorem

Yêu cầu

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

Nội dung khoá học

10 sections

Signals

41 lectures
Unit impulse Function - Elementary Signals
08:00
Deterministic and Random Signals
04:31
Analog and Digital Signals
04:31
Unit Ramp and Parabolic & Singularity Functions
06:03
Unit step Function
05:53
Exponential Functions - Elementary Signals
04:24
Signum Function - Elementary Signals
02:04
Rectangular Function - Elementary Signals
03:08
Triangular Function - Elementary Signals
04:56
Sinusoidal Functions - Elementary Signals
02:27
Sinc & Sampling Functions - Elementary Signals
04:18
Periodic & Non Periodic Signals- Classification
28:18
Even and Odd Signals
17:33
Causal and Non Causal Signals
05:07
Rectangular Function E & P
03:49
Unit step Function E & P
03:45
Unit Ramp Function E & P
03:51
Power of Sinusoidal Signal
05:49
Energy and Power Signals
03:26
Effect of shifting and Scaling on E & P
04:54
Observation Points on E & P
07:21
Operations on Independent Variable of Signal
15:45
GATE Previous Problems with Solutions Set - 1
17:57
GATE Previous Problems with Solutions Set - 2
08:49
IES Discussion Part - 1
05:14
IES Discussion Part - 2
03:37
IES Discussion Part - 3
02:18
IES Discussion Part - 4
01:57
IES Discussion Part - 5
03:59
IES Discussion Part - 6
03:30
IES Discussion Part - 7
02:28
IES Discussion Part - 8
01:49
IES Discussion Part - 9
01:44
IES Discussion Part - 10
01:55
IES Discussion Part - 11
03:59
IES Discussion Part - 12
03:06
IES Discussion Part - 13
04:54
IES Discussion Part - 14
02:21
IES Discussion Part - 15
02:46
IES Discussion Part - 16
03:29
IES Discussion Part - 17
02:09

Systems

38 lectures
Systems Classification - Linear & Nonlinear Systems
28:57
Systems Classification - Time Variant & time Invariant Systems
18:37
Static & Dynamic & Causal & Non Causal Systems
04:51
Examples
07:22
Stable & Unstable Systems
03:24
Examples
05:26
Invertible & Non Invertible Systems
05:31
GATE Previous Problems with Solutions Set - 1
15:18
GATE Previous Problems with Solutions Set - 2
12:19
GATE Previous Problems with Solutions Set - 3
21:05
IES Discussion Part - 1
04:50
IES Discussion Part - 2
07:22
IES Discussion Part - 3
06:31
IES Discussion Part - 4
06:08
IES Discussion Part - 5
02:42
IES Discussion Part - 6
04:25
IES Discussion Part - 7
04:26
IES Discussion Part - 8
02:02
IES Discussion Part - 9
02:41
IES Discussion Part - 10
06:42
IES Discussion Part - 11
04:13
IES Discussion Part - 12
03:08
IES Discussion Part - 13
04:55
IES Discussion Part - 14
02:21
IES Discussion Part - 15
02:46
IES Discussion Part - 16
06:04
IES Discussion Part - 17
03:26
IES Discussion Part - 18
05:39
IES Discussion Part - 19
03:02
IES Discussion Part - 20
03:35
IES Discussion Part - 21
02:53
LIT systems with Properties - 1
01:37
LIT systems with Properties - 2
02:20
LIT systems with Properties - 3
03:47
LIT systems with Properties - 4
03:49
LIT systems with Properties - 5
02:34
LIT systems with Properties - 6
04:55
LIT systems with Properties - 7
05:33

Fourier Series

24 lectures
Fourier Series Introduction
06:09
Orthogonality in Vectors
06:28
Orthogonality in Signals
08:28
Orthogonal Signal Space & Signal Approximation
11:34
Mean Square Error and Complete Set
07:19
Orthonormal Set
05:35
Complete Set Example - 1
11:43
Complete Set Example - 2
06:12
Orthogonality in Complex Functions
04:11
Full Wave Rectified signal EFS
08:44
Dirichlet's Conditions for Fourier Series
03:58
TFS and EFS Expansion Example
13:41
Symmetric Conditions
08:13
Check the Symmetry Conditions for Examples
21:46
Exponentials periodic signal TFS & EFS
07:17
Triangular Periodic Signal TFS & EFS
14:48
Frequency Spectrum
04:21
GATE Previous Problems with Solutions Set - 1
14:08
GATE Previous Problems with Solutions Set - 2
20:45
IES Discussion Part - 1
03:41
IES Discussion Part - 2
04:40
IES Discussion Part - 3
04:27
IES Discussion Part - 4
03:55
IES Discussion Part - 5
07:23

Fourier Transform

35 lectures
Introduction to Fourier Transforms & Dirichlet s conditions
09:41
Fourier Transform of Unit Impulse function and One sided Exponential.
13:52
Fourier Transform of Two sided Exponential
08:40
Fourier Transform of Signum Function
07:43
Fourier Transform of Unit Step function & Sinusoidal Functions
06:22
Fourier Transform of Rectangular & Sinc & Fampling Functions
15:01
Fourier Transform of Triangular Function
10:07
Fourier Transform of Trapezoidal Signal
05:51
Linearity property of Fourier Transform
05:07
Time scaling property of Fourier Transform
05:34
Time shifting property of Fourier Transform
04:41
Frequency shifting property of Fourier Transform
04:07
Differentiation in Time property of Fourier Transform
05:29
Integration in Time domain Property of Fourier Transform
06:20
Differentiation in Frequency domain Property of Fourier Transform
05:01
Conjugation Property of Fourier Transform
04:22
Duality Property of Fourier Transform
03:46
Modulation Property of Fourier Transform
05:39
Area Under time and Frequency Domain Signals
08:38
Time Convolution Property of Fourier Transform
07:56
Frequency Convolution Property of Fourier Transform
08:54
Parseval's relation
08:02
Fourier Transform of Periodic Signal
06:39
Hilbert Transform
16:06
Hilbert Transform Example
08:10
Frequency Spectrum
11:06
GATE Previous Problems with Solutions Set - 1
11:40
GATE Previous Problems with Solutions Set - 2
17:09
IES Discussion Part - 1
02:23
IES Discussion Part - 2
03:31
IES Discussion Part - 3
03:28
IES Discussion Part - 4
02:47
IES Discussion Part - 5
02:47
IES Discussion Part - 6
05:07
IES Discussion Part - 7
06:25

Laplace Transform

33 lectures
Laplace Transform of impulse function with ROC
05:24
LT of unit step Function with ROC
02:47
LT of left side unit step Function with ROC
03:54
LT of Exponential Functions with ROC
06:58
LT of Complex Exponentials & cos and sin Functions with ROC
07:43
LT and ROC of both side Exponentials
06:33
LT and ROC of damped sin Function
05:02
LT and ROC of Damped cos Function
03:38
LT and ROC of Hyperbolic sin and cos Functions
03:18
Linearity Property of LT
04:01
Time shifting Property of LT
05:56
Frequency shifting Property of LT
04:40
Time scaling and Time Reversal Property of LT
07:37
Time Differentiation Property of LT
05:02
Differentiation in S-domain Property of LT
03:51
Conjugation property of LT
04:14
Initial and Final value Theorems of LT
05:53
Convolution Property of LT
05:06
GATE Previous Problems with Solutions Set - 1
08:37
GATE Previous Problems with Solutions Set - 2
07:23
GATE Previous Problems with Solutions Set - 3
05:30
GATE Previous Problems with Solutions Set - 4
07:03
GATE Previous Problems with Solutions Set - 5
03:21
GATE Previous Problems with Solutions Set - 6
07:52
GATE Previous Problems with Solutions Set - 7
07:02
GATE Previous Problems with Solutions Set - 8
05:50
GATE Previous Problems with Solutions Set - 9
04:44
Laplace Transform Example Set - 1
12:54
Laplace Transform Example Set - 2
14:11
IES Discussion Part - 1
06:44
IES Discussion Part - 2
04:20
IES Discussion Part - 3
06:20
IES Discussion Part - 4
05:59

Z-Transform

23 lectures
Z-Transform and ROC of unit impulse and step Functions
05:03
ZT and ROC of u(-n) and -u(-n-1)
08:38
ZT and ROC of exponentials a^nu(n) and -a^nu(-n-1)
06:33
ZT and ROC of complex exponentials and coswn.u(n)
07:49
ZT and ROC of sinwn.u(n)
02:41
ZT Properties - Linearity
03:36
ZT Properties - Time shifting
03:03
ZT properties - Multiplication with exponential
03:40
ZT Properties - Time Reversal
02:57
ZT Properties - Time Expansion
02:53
ZT Properties - Differentiation in Z-Domain
04:10
ZT Properties - Conjugation
02:59
ZT Properties - Convolution
05:11
ZT Properties - Initial value Theorem
03:02
ZT Properties - Final value Theorem
04:30
GATE Previous Problems with Solutions Set - 1
14:19
GATE Previous Problems with Solutions Set - 2
12:42
GATE Previous Problems with Solutions Set - 3
11:25
IES Discussion Part - 1
04:58
IES Discussion Part - 2
04:13
IES Discussion Part - 3
04:11
IES Discussion Part - 4
07:39
IES Discussion Part - 5
04:57

Discrete Time Fourier Transform (DTFT)

7 lectures
DTFT(Discrete Time Fourier Transform)
04:38
DTFT of Impulse & Unit step Functions
04:11
DTFT of DT Exponential Sequence
02:46
DFT-Discrete Fourier Transform
02:45
DFT Example
09:45
GATE Previous Problems with Solutions Set - 1
16:09
GATE Previous Problems with Solutions Set - 2
15:20

Sampling Theorem

4 lectures
Sampling Theorem Definition
03:30
Nyquist Condition - NR Calcutions
09:21
Time Domain & Frequency Domain Analysis(spectral)
21:54
GATE Previous Problems with Solutions Set - 1
16:55

Signal Transmission Through LTI System

4 lectures
Distortionless transmission system and frequency respons
06:17
Impulse Response of Distortionless transmission system
09:28
Filter Characteristics of LTI Systems
06:08
Signal Bandwidth vs System Bandwidth
08:06

Convolution & Correlation

10 lectures
Convolution & Examples
19:00
Convolution Graphical procedure exponential with unit step
06:22
Convolution Graphical procedure two rectangular signals
10:32
Triangular and rectangular convolution
09:29
Correlation Introduction
07:39
Convolution vs Correlation
10:05
Input Output PSD
07:56
Graphical Correalation
05:58
PSD Problems
03:45
ACF vs PSD
07:55

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