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2: Linear Systems

Last updated

Apr 23, 2021
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- 1.1: Introduction to Course
- 2.1: Definition of a System

Franz S. Hover & Michael S. Triantafyllou
Massachusetts Institute of Technology via MIT OpenCourseWare

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2.1: Definition of a System
What is a system? Why is it important to create system models, especially mathematical ones?
2.2: Time-Invariant Systems
Defines a time-invariant system. Provides method for assessing whether a system is time-invariant or not.
2.3: Linear Systems
Defines linearity of a system and outlines the importance of linear, time-invariant (LTI) systems in modeling real-world situations.
2.4: The Impulse Response and Convolution
Defines the response of an LTI system to an input as the convolution of that input and the system's impulse response function.
2.5: Causal Systems
Adaptation of the convolution expression to account only for response after the input has been applied (after t=0), which is useful for analyzing physical systems.
2.6: An Example of Finding the Impulse Response
How to define a LTI system by finding the impulse response for its differential equation.
2.7: Complex Numbers
The connection between a complex number and complex exponential (De Moivre's theorem), and how this allows a complex number to be visualized in the Cartesian plane.
2.8: Fourier Transform
The Fourier transform is the underlying principle for frequency-domain description of signals: it allows a time-domain signal to be transformed into a (complex) frequency-domain version, and to be transformed back as necessary.
2.9: The Angle of a Transfer Function
Useful properties of the Fourier (and Laplace) transforms, involving the magnitude and angle of the transfer function.
2.10: The Laplace Transform
A basic overview of the role of the Laplace transform in analyzing dynamic systems, the Convolution Theorem, and in solving differential equations.

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