# Signals and Systems

## by MIT

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#### Course Description

This course was developed in 1987 by the MIT Center for Advanced Engineering Studies. It was designed as a distance-education course for engineers and scientists in the workplace.

Signals and Systems is an introduction to analog and digital signal processing, a topic that forms an integral part of engineering systems in many diverse areas, including seismic data processing, communications, speech processing, image processing, defense electronics, consumer electronics, and consumer products.

The course presents and integrates the basic concepts for both continuous-time and discrete-time signals and systems. Signal and system representations are developed for both time and frequency domains. These representations are related through the Fourier transform and its generalizations, which are explored in detail. Filtering and filter design, modulation, and sampling for both analog and digital systems, as well as exposition and demonstration of the basic concepts of feedback systems for both analog and digital systems, are discussed and illustrated.

Signals and Systems is an introduction to analog and digital signal processing, a topic that forms an integral part of engineering systems in many diverse areas, including seismic data processing, communications, speech processing, image processing, defense electronics, consumer electronics, and consumer products.

The course presents and integrates the basic concepts for both continuous-time and discrete-time signals and systems. Signal and system representations are developed for both time and frequency domains. These representations are related through the Fourier transform and its generalizations, which are explored in detail. Filtering and filter design, modulation, and sampling for both analog and digital systems, as well as exposition and demonstration of the basic concepts of feedback systems for both analog and digital systems, are discussed and illustrated.

This content is provided under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 license.

Name | Description | Time | Price | ||
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1 | Lecture 1, Introduction | This lecture gives a general introduction to the Signals and Systems course, with demonstrations of a feedback system used to stabilize an inverted pendulum and digital signal processing used to remove distortions from a musical recording. | 30:25 | Free | View In iTunes |

2 | Lecture 1: Introduction | -- | -- | Free | View In iTunes |

3 | Lecture 2, Signals and Systems: Part I | This lecture covers mathematical representation of signals and systems, including transformation of variables and basic properties of common signals. | 44:07 | Free | View In iTunes |

4 | Lecture 2: Signals and systems: part I | -- | -- | Free | View In iTunes |

5 | Lecture 3, Signals and Systems: Part II | This video covers the the unit step and impulse signals. System properties are discussed, including memory, invertibility, causality, stability, and time invariance. | 53:08 | Free | View In iTunes |

6 | Lecture 3: Signals and systems: part II | -- | -- | Free | View In iTunes |

7 | Lecture 4, Convolution | This lecture video discusses representation of signals in terms of impulses. Linear, time-invariant (LTI) systems, properties and representation. | 52:16 | Free | View In iTunes |

8 | Lecture 4: Convolution | -- | -- | Free | View In iTunes |

9 | Lecture 5, Properties of Linear, Time-invariant Systems | This video lecture covers properties of linear, time-invariant systems, including the commutative, associative, and distributive properties. Also covers systems in cascade and parallel combinations.... | 55:02 | Free | View In iTunes |

10 | Lecture 5: Properties of linear, time-invariant systems | -- | -- | Free | View In iTunes |

11 | Lecture 6, Systems Represented by Differential Equations | This lecture covers mathematical representation of signals and systems, including transformation of variables and basic properties of common signals. | 47:14 | Free | View In iTunes |

12 | Lecture 6: Systems represented by differential and difference equations | -- | -- | Free | View In iTunes |

13 | Lecture 7, Continuous-Time Fourier Series | This video lecture discusses continuous-time Fourier serires, and the response of continuous-time LTI systems to complex exponentials. Also covered: the eigenfunction property. | 51:06 | Free | View In iTunes |

14 | Lecture 7: Continuous-time Fourier series | -- | -- | Free | View In iTunes |

15 | Lecture 8, Continuous-Time Fourier Transform | This video covers many uses and applications of Fourier transforms in signal processing. We will derive the Fourier transform representation of aperiodic signals, and examine the relationship between Fourier series and Fourier transforms. | 35:27 | Free | View In iTunes |

16 | Lecture 8: Continuous-time Fourier transform | -- | -- | Free | View In iTunes |

17 | Lecture 9, Fourier Transform Properties | This video covers Fourier transform properties, including linearity, symmetry, time shifting, differentiation, and integration. We will also cover convolution and modulation properties and how they can be used for filtering, modulation, and sampling. | 49:23 | Free | View In iTunes |

18 | Lecture 9: Fourier transform properties | -- | -- | Free | View In iTunes |

19 | Lecture 10, Discrete-Time Fourier Series | This lecture will discuss the similarities and differences with discrete-time and continuous-time Fourier series. Analysis and synthesis equations, and approximation of periodic and aperiodic signals. | 50:21 | Free | View In iTunes |

20 | Lecture 10: Discrete-time Fourier series | -- | -- | Free | View In iTunes |

21 | Lecture 11, Discrete-Time Fourier Transform | This video gives a summary of relationships between continuous-time and discrete-time Fourier series and Fourier transforms. | 55:58 | Free | View In iTunes |

22 | Lecture 11: Discrete-time Fourier transform | -- | -- | Free | View In iTunes |

23 | Lecture 12, Filtering | Demonstration: a look at filtering in a commercial audio control room. Covers many types of filters: selective filters, moving average filters, low-pass and high-pass filters, and commercial applications. | 41:54 | Free | View In iTunes |

24 | Lecture 12: Filtering | -- | -- | Free | View In iTunes |

25 | Lecture 13, Continuous-Time Modulation | In this lecture we will cover continuous-time modulation: sinusoidal amplitude modulation, synchronous and asynchronous demodulation. We will discuss communication applications, such as frequency-division multiplexing and single-side band modulation. | 53:46 | Free | View In iTunes |

26 | Lecture 13: Continuous-time modulation | -- | -- | Free | View In iTunes |

27 | Lecture 14, Demonstration of Amplitude Modulation | Lecture 14, Demonstration of Amplitude Modulation. Demonstration with Professor Sandy Hill from the University of Massachusetts at Amherst. RC audio generator, oscilloscope, and spectrum analyzer demonstrations with speech and radio. | 35:43 | Free | View In iTunes |

28 | Lecture 14: Demonstration of amplitude modulation | -- | -- | Free | View In iTunes |

29 | Lecture 15, Discrete-Time Modulation | Discussion of complex exponential and sinusoidal modulation for discrete-time signals. Introduction and analysis of pulse carriers in continuous-time, sampling theorem. | 42:55 | Free | View In iTunes |

30 | Lecture 15: Discrete-time modulation | -- | -- | Free | View In iTunes |

31 | Lecture 16, Sampling | This lecture we will discuss sampling to reconstruct the output of a sinusoidal oscillator and the effect of undersampling: aliasing. This includes a visit to Doc Harold Edgerton's MIT Strobe Laboratory to demonstrate cases where aliasing can be useful. | 46:08 | Free | View In iTunes |

32 | Lecture 16: Sampling | -- | -- | Free | View In iTunes |

33 | Lecture 17, Interpolation | In this lecture we will see how linear interpolation is used to reconstruct a signal from its sample. Reconstructing a signal by processing an impulse train with a low-pass filter. | 52:36 | Free | View In iTunes |

34 | Lecture 17: Interpolation | -- | -- | Free | View In iTunes |

35 | Lecture 18, Discrete-Time Processing of Continuous-Time Signals | In this lecture we will learn how to use sampling to convert continuous-time signals into discrete-time signals for processing. We will also demonstrate how to reconstruct a signal by processing an impulse train with a low-pass filter. | 39:39 | Free | View In iTunes |

36 | Lecture 18: Discrete-time processing of continuous-time signals | -- | -- | Free | View In iTunes |

37 | Lecture 19, Discrete-Time Sampling | This lecture compares discrete-time and continuous-time sampling, and the differences between down-sampling (decimation) and up-sampling (reconstruction of original sequence). | 49:23 | Free | View In iTunes |

38 | Lecture 19: Discrete-time sampling | -- | -- | Free | View In iTunes |

39 | Lecture 20, The Laplace Transform | This video covers the Laplace transform, in particular its relation to the Fourier transform. We will see cover regions of convergence, poles and zeroes, and inverse transforms using partial fraction expansion. | 54:49 | Free | View In iTunes |

40 | Lecture 20: The Laplace transform | -- | -- | Free | View In iTunes |

41 | Lecture 21, Continuous-Time Second-Order Systems | Characteristics of second-order systems, geometric evaluation of frequency responses from pole-zero plots, system function for first-order and second-order systems. Overdamped and underdamped systems, a demonstration of these systems for speech synthesis. | 42:52 | Free | View In iTunes |

42 | Lecture 21: Continuous-time second-order systems | -- | -- | Free | View In iTunes |

43 | Lecture 22, The z-Transform | This lecture covers the z-Transform with linear time-invariant systems. We will discuss the relationship to the discrete-time Fourier trasform, region of convergence (ROC), and geometric evaluation of the Fourier transform from the pole-zero plot. | 51:43 | Free | View In iTunes |

44 | Lecture 22: The z-transform | -- | -- | Free | View In iTunes |

45 | Lecture 23, Mapping Continuous-Time Filters to Discrete-Time Filters | In this lecture we wil continue our discussion of properties of the z-transform. Covers systems characterized by linear constant-coefficient difference equations, and transformations between continuous-time and discrete-time systems. | 50:26 | Free | View In iTunes |

46 | Lecture 23: Mapping continuous-time filters to discrete-time filters | -- | -- | Free | View In iTunes |

47 | Lecture 24, Butterworth Filters | This lecture we cover Butterworth filters, including: parameters, cutoff frequency, filter order, and distribution of poles. Also covers the design of a discrete-time Butterwoth filter using impulse invariance, and also using the bilinear transformation. | 45:12 | Free | View In iTunes |

48 | Lecture 24: Butterworth filters | -- | -- | Free | View In iTunes |

49 | Lecture 25, Feedback | In this lecture we will discuss feedback systems, applications and consequences. Feedback can cause destabilization, but also be used to stabilize unstable systems through inverse system design, compensation for nonideal elements, and root-locus analysis. | 44:53 | Free | View In iTunes |

50 | Lecture 25: Feedback | -- | -- | Free | View In iTunes |

51 | Lecture 26, Feedback Example: The Inverted Pendulum | This video covers the open loop system and explores choices for feedback dynamics. We will use proportional and derivative feedback to reach pendulum stability. Demonstration of an inverted pendulum on a track, and the effect of changing system dynamics. | 34:41 | Free | View In iTunes |

52 | Lecture 26: Feedback example: the inverted pendulum | -- | -- | Free | View In iTunes |

53 | Problem set 1: Introduction | -- | -- | Free | View In iTunes |

54 | Problem set solution 1: Introduction | -- | -- | Free | View In iTunes |

55 | Problem set 2: Signals and systems: part I | -- | -- | Free | View In iTunes |

56 | Problem set solution 2: Signals and systems: part I | -- | -- | Free | View In iTunes |

57 | Problem set 3: Signals and systems: part II | -- | -- | Free | View In iTunes |

58 | Problem set solution 3: Signals and systems: part II | -- | -- | Free | View In iTunes |

59 | Problem set 4: Convolution | -- | -- | Free | View In iTunes |

60 | Problem set solution 4: Convolution | -- | -- | Free | View In iTunes |

61 | Problem set 5: Properties of linear, time-invariant systems | -- | -- | Free | View In iTunes |

62 | Problem set solution 5: Properties of linear, time-invariant systems | -- | -- | Free | View In iTunes |

63 | Problem set 6: Systems represented by differential and difference equations | -- | -- | Free | View In iTunes |

64 | Problem set solution 6: Systems represented by differential and difference equations | -- | -- | Free | View In iTunes |

65 | Problem set 7: Continuous-time Fourier series | -- | -- | Free | View In iTunes |

66 | Problem set solution 7: Continuous-time Fourier series | -- | -- | Free | View In iTunes |

67 | Problem set 8: Continuous-time Fourier transform | -- | -- | Free | View In iTunes |

68 | Problem set solution 8: Continuous-time Fourier transform | -- | -- | Free | View In iTunes |

69 | Problem set 9: Fourier transform properties | -- | -- | Free | View In iTunes |

70 | Problem set solution 9: Fourier transform properties | -- | -- | Free | View In iTunes |

71 | Problem set 10: Discrete-time Fourier series | -- | -- | Free | View In iTunes |

72 | Problem set solution 10: Discrete-time Fourier series | -- | -- | Free | View In iTunes |

73 | Problem set 11: Discrete-time Fourier transform | -- | -- | Free | View In iTunes |

74 | Problem set solution 11: Discrete-time Fourier transform | -- | -- | Free | View In iTunes |

75 | Problem set 12: Filtering | -- | -- | Free | View In iTunes |

76 | Problem set solution 12: Filtering | -- | -- | Free | View In iTunes |

77 | Problem set 13: Continuous-time modulation | -- | -- | Free | View In iTunes |

78 | Problem set solution 13: Continuous-time modulation | -- | -- | Free | View In iTunes |

79 | Problem set 14: Demonstration of amplitude modulation | -- | -- | Free | View In iTunes |

80 | Problem set solution 14: Demonstration of amplitude modulation | -- | -- | Free | View In iTunes |

81 | Problem set 15: Discrete-time modulation | -- | -- | Free | View In iTunes |

82 | Problem set solution 15: Discrete-time modulation | -- | -- | Free | View In iTunes |

83 | Problem set 16: Sampling | -- | -- | Free | View In iTunes |

84 | Problem set solution 16: Sampling | -- | -- | Free | View In iTunes |

85 | Problem set 17: Interpolation | -- | -- | Free | View In iTunes |

86 | Problem set solution 17: Interpolation | -- | -- | Free | View In iTunes |

87 | Problem set 18: Discrete-time processing of continuous-time signals | -- | -- | Free | View In iTunes |

88 | Problem set solution 18: Discrete-time processing of continuous-time signals | -- | -- | Free | View In iTunes |

89 | Problem set 19: Discrete-time sampling | -- | -- | Free | View In iTunes |

90 | Problem set solution 19: Discrete-time sampling | -- | -- | Free | View In iTunes |

91 | Problem set 20: The Laplace transform | -- | -- | Free | View In iTunes |

92 | Problem set solution 20: The Laplace transform | -- | -- | Free | View In iTunes |

93 | Problem set 21: Continuous-time second-order systems | -- | -- | Free | View In iTunes |

94 | Problem set solution 21: Continuous-time second-order systems | -- | -- | Free | View In iTunes |

95 | Problem set 22: The z-transform | -- | -- | Free | View In iTunes |

96 | Problem set solution 22: The z-transform | -- | -- | Free | View In iTunes |

97 | Problem set 23: Mapping continuous-time filters to discrete-time filters | -- | -- | Free | View In iTunes |

98 | Problem set solution 23: Mapping continuous-time filters to discrete-time filters | -- | -- | Free | View In iTunes |

99 | Problem set 24: Butterworth filters | -- | -- | Free | View In iTunes |

100 | Problem set solution 24: Butterworth filters | -- | -- | Free | View In iTunes |

101 | Problem set 25: Feedback | -- | -- | Free | View In iTunes |

102 | Problem set solution 26: Feedback | -- | -- | Free | View In iTunes |

103 | Problem set 26: Feedback example: the inverted pendulum | -- | -- | Free | View In iTunes |

104 | Problem set solution 26: Feedback example: the inverted pendulum | -- | -- | Free | View In iTunes |

104 Items |

#### Customer Reviews

##### wow

exactly what i have been looking for!

##### Not to bad

Lot of useful info. Read a book might learn something lol