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2: Linear Systems

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  • Page ID
    47225
    • Franz S. Hover and 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.

    This page titled 2: Linear Systems was last modified on Fri, 23 Apr 2021 05:53:01 GMT and is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Franz S. Hover and Michael S. Triantafyllou (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform.