Signals and Systems

Undergraduate course on signals and systems.

Course Information

Instructor: Ulugbek S. Kamilov
Institution: Washington University in St. Louis
Term: Spring 2025

Course Description

Signals and systems studies how signals represent information and how systems process, transform, and transmit them. This course introduces the mathematical and computational foundations of signal analysis and linear systems, with an emphasis on time- and frequency-domain representations, convolution, Fourier analysis, and system properties.

Lecture Topics

  1. Introduction to Signals and Systems
  2. Continuous-Time and Discrete-Time Signals
  3. Fundamental Signals and Signal Operations
  4. Introduction to Systems and Their Properties
  5. Linear Time-Invariant (LTI) Systems: Convolution
  6. Linear Time-Invariant (LTI) Systems: Properties
  7. Linear Differential and Difference Equations
  8. Hilbert Spaces and Orthogonality
  9. Continuous-Time Fourier Series (CTFS)
  10. Discrete-Time Fourier Series (DTFS)
  11. Continuous-Time Fourier Transform
  12. Properties of the Fourier Transform
  13. Parseval’s Theorem and Signal Truncation
  14. Fourier Analysis of LTI Systems
  15. Discrete-Time Fourier Transform (DTFT)
  16. Properties of the DTFT
  17. Sampling and Reconstruction
  18. Applications to Communication Systems
  19. Laplace Transform: Definition and Properties
  20. Laplace Transform: Region of Convergence
  21. Laplace Transform: Partial Fraction Expansion
  22. Inverse Laplace Transform
  23. Z-Transform: Definition and Properties
  24. Z-Transform: Region of Convergence and Inversion