ECE 101 Lecture Supplement: Linear Systems Fundamentals
R. L. Cruz
University of California, San Diego
rcruz@ucsd.edu
(c) Copyright 1996

These notes are intended to provide an abridged summary of selected lectures, as well as to provide supplemental information to the lectures.

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• Contents
• Models of Systems
  • Causal Systems
  • Linear Time Invariant Systems
  • Stable and Unstable Systems
• Transfer Functions and Frequency Response of LTI systems
  • Complex Exponential Signals
  • Response of LTI Systems to Complex Exponentials
  • Determination of Stability from Transfer Function
• Impulse Response of LTI Systems
  • Impulses
  • Impulse Response of LTI Systems
  • Convolution
  • Relationship between Impulse Response and Transfer Function
  • Relationship between Impulse Response and Frequency Response
  • Determination of Stability from Impulse Response
  • Determination of Causality from Impulse Response
• Basic Signal Analysis
  • Continuous Time Periodic Signals: The Fourier Series
  • Discrete Time Periodic Signals: The D.T. Fourier Series
  • Continuous Time Aperiodic Signals: The Fourier Transform
  • Discrete Time Aperiodic Signals: The D.T. Fourier Transform
  • Unbounded Continuous Time Aperiodic Signals: The Laplace Transform
  • Unbounded Discrete Time Aperiodic Signals: The z-transform
• Appendix
  • Analytic Functions
  • Example: A Low Pass Filtered Square Wave