Continuous- and Discrete-Time Signals and Systems

Table of Contents

Part 1: Continuous Signals and Systems

  • Signals
    • Standard Signals
    • Operations
  • Characterization of Systems in the Time Domain
    • Impulse Response
    • Convolution
    • Step Response
    • Eigenfunctions and the Transfer Function
    • Example: Analysis of a Passive Electrical Network
    • Example: Analysis of a Damped Spring Pendulum
  • The Laplace-Transform
    • Definition
    • Properties
    • Theorems
    • Summary of Properties, Theorems and Transforms
    • Inverse Transform
    • Analysis of Passive Electrical Networks
  • The Fourier Transform
    • Definition
    • Properties
    • Theorems
    • Summary of Properties, Theorems and Transforms
  • Characterization of Systems in the Spectral Domain
    • The Transfer Function
    • The Bode Plot
    • Phase and Group Delay
    • Combination of Systems
  • Properties of LTI-Systems
    • Causality and Stability
    • Classes of Systems
    • Idealized Systems
  • Periodic Signals
    • Spectrum
    • Relation between Spectrum and Fourier Series
    • Convolution of a Periodic with an Aperiodic Signal
  • Sampling of Signals
    • Ideal Sampling and Reconstruction

Part 2: Time-Discrete Signals and Systems

  • Discrete Signals
    • Standard Signals
    • Operations
  • Characterization of Discrete Systems in the Time Domain
    • Difference Equation
    • Impulse Response
    • Linear Convolution
    • Example: Convolution of an Audio Signal with a Room Impulse Response
    • Eigenfunctions and the Transfer Function
  • The z-Transform
    • Definition
    • Properties
    • Theorems
    • Summary of Properties, Theorems and Transforms
  • The Discrete-Time Fourier Transform
    • Definition
    • Properties
    • Theorems
    • Summary of Properties, Theorems and Transforms
  • The Discrete Fourier Transform
    • Definition
    • Properties
    • Theorems
    • Summary of Properties, Theorems and Transforms
    • The Fast Fourier Transform
    • Fast Convolution
  • Characterization of Discrete Systems in the Spectral Domain
    • The Transfer Function
    • Example: Measurement of an Electroacoustic Transfer Function
    • Magnitude and Phase
    • Phase and Group Delay
    • Combination of Systems
  • Properties of Discrete LTI-Systems

References

See the original lecture for a detailed list of references.

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