Signals and Systems

Unit 1: Laplace transform and z-transform (43 topics)
Unit 2: The fourier transform (37 topics)
Unit 3: systems (17 topics)
Unit 4: time and frequency domain analysis of systems (19 topics)
Unit 5: signals (15 topics)
total: 131 topics

1-Laplace Transform

* (khan academy) https://www.youtube.com/watch?v=OiNh2DswFt4
* (hindi) https://www.youtube.com/watch?v=W0Qb6PMAOX8
* (engineering math) https://www.youtube.com/watch?v=8oE1shAX96U
* (Laplace Transform Explained and Visualized Intuitively) (Physics Videos by Eugene Khutoryansky) https://www.youtube.com/watch?v=6MXMDrs6ZmA
* (The Laplace Transform - A Graphical Approach) (Brian Douglas) https://www.youtube.com/watch?v=ZGPtPkTft8g

2-The region of convergence of the laplace transform

* (Gowthami Swarna) https://www.youtube.com/watch?v=pJYoGL9hMlM
* (example 1) https://www.youtube.com/watch?v=ptpkDCi3Ux4
* (neso academy) (roc and its properties) https://www.youtube.com/watch?v=LyOQVvPVIuE
* (neso academy) (shortcut for region of convergence) https://www.youtube.com/watch?v=RfKpZqaKn6s
* (engineering funda) (71) (Region of convergence ROC basics, properties and examples in Laplace transform) https://www.youtube.com/watch?v=3BX-_AK0iSg

3-Poles and zeros in the laplace transform

* (Laplace poles and zeros) https://www.youtube.com/watch?v=WzeqWEmYHvM
* (Laplace transform poles and zeros) https://www.youtube.com/watch?v=jIEQsanGSf4
* (intro to control - poles and zeros) https://www.youtube.com/watch?v=Em5TuH4TVr4
* (hindi) https://www.youtube.com/watch?v=un0xFrY2zU0
* (how to plot a pole zero diagram and verify stability) https://www.youtube.com/watch?v=ifoiXh01eaY

4-properties of the roc of the laplace transform

5-laplace transforms of some common signals

6-properties of the laplace transform

7-the inverse laplace transform

8-partial fraction expansion in laplace transform

9-the system function of the laplace transform

10-characterization of LTI systems

11-system function for LTI systems described by linear constant-coefficient differential equations

12-systems interconnection

13-the unilateral laplace transform

14-transform circuits of the laplace transform

15-graphical understanding of ROC

16-the Z-transform

17-the region of convergence of Z-transform

18-properties of the ROC of the Z-transform

19-Z-transforms of some common signals

20-properties of the z-transform

21-the inverse z-transform

22-power series expansion of z-transform

23-the system function of the z-transform

24-characterization of discrete-time LTI systems in z-transform

25-system function for LTI systems described by linear constant-coefficient difference equations

26-the unilateral z-transform

27-initial value theorem of the laplace transform

28-final value theorem of the laplace transform

29-convolution in time domain property of the laplace transform

30-the laplace transform of the ramp function

31-the laplace transform of a pulse

32-the laplace transform of a linear segment

33-the laplace transform of a triangular waveform

34-the laplace transform of a rectangular periodic waveform

35-the laplace transform of a half-rectified sine waveform

36-initial value theorem of the z-transform

37-final value theorem of the z-transform

38-the z-transform of the geometric sequence

39-the z-transform of the discrete-time unit step function

40-the z-transform of the discrete-time cosine and sine functions

41-the z-transform of the discrete-time unit ramp function

42-computation of the z-transform with contour integration

43-s to z plane mapping

--- Unit 2: The fourier transform: topics 44-80 ---

44-The fourier transform

45-fourier transform pair

46-connection between the fourier transform and the laplace transform

47-properties of the continuous time fourier transform

48-frequency response of the continuous LTI system

49-real time functions

50-imaginary time functions

51-the cosine and sine function pair

52-the signum function pair

53-the unit step function pair

54-the delta funtion pair

55-the constant function pair

56-parseval's theorem

57-conjugate time and frequency functions

58-the time convolution & frequency convolution

59-the area under f(t) and F(w)

60-the discrete time fourier transform

61-the discrete time fourier spectra

62-connection between the discrete time fourier transform and the z-transform

63-properties of the discrete time fourier transform

64-the frequency response of discrete time LTI systems

65-system response to sampled continuous time sinusoids

66-simulation

67-discrete time fourier transform pair

68-the weak dirichlet condition

69-the strong dirichlet conditions

70-Gibb's phenomena

71-Derivation of the fourier transform from the laplace transform

72-the fourier transform of the periodic time function

73-the fourier transform of the periodic time function with period t

74-fourier series

75-fourier series representation of periodic signals

76-trigonometric fourier series

77-convergence of fourier series

78-discrete fourier series

79-discrete fourier series transformation

80-properties of discrete fourier series

--- Unit 3: Systems: topics 81-96 ---
81-LTI systems characterized by differential equations in discrete form
82-response of a continuous time LTI system and the convolution integral
83-properties of the convolution integral
84-properties of continuous time LTI systems
85-systems described by differential equations
86-response of a discrete time LTI system
87-properties of the convolution sum
88-properties of discrete time LTI systems
89-eigen functions of continuous time LTI systems and discrete time LTI systems
90-systems described by difference equations in discrete form
91-state space representation of continuous time LTI systems
92-solutions of state equations for discrete time LTI systems
93-solutions of state equations for continuous time LTI systems
94-system representation
95-classification of the system
96-properties of the system

--- Unit 4: Time and frequency domain analysis of systems: topics 97-115 ---
97-systems in the time domain
98-continuous time convolution
99-examples of the continuous time convolution
100-properties of convolution
101-discrete time convolution
102-convolution through time
103-system function
104-stability and causality
105-realizable systems
106-inverse systems
107-unit sample response for rational system functions
108-frequency response for rational system functions
109-systems with linear phase
110-types of the linear phase system
111-the z-transform of linear phase systems
112-all pass filters
113-minimum phase systems
114-feedback systems
115-discrete time systems in the time domain

--- Unit 5: Signals: topics 116-130 ---

116-the unit step signal
117-the unit ramp function
118-the delta function
119-the sampling property of the delta function
120-the sifting property of the delta function
121-useful signals
122-the complex exponential
123-the impulse function
124-discrete time impulse (unit sample)
125-BIBO stability
126-discrete time signals
127-signal duration of a discrete time signal
128-signal manipulations
129-classification of signals
130-signals