Signals and systems

Materials I developed for a course I helped teach on signals and systems.

Table of Contents

1. Reasoning about LTI systems
   • LTI systems
   • Invertibility
   • Impulse response
2. More discrete systems
   • Cascade systems
   • Convolution sum
3. Continuous-time systems
   • Continuous-time systems
   • Convolution integral
4. Periodic signals
   • Periodic signals
   • Fourier series expansion
   • Step response
5. Causality, stability, and duality
   • Causality
   • BIBO stability
   • Duality
   • Properties of Fourier series coefficients
6. Properties of Fourier coefficients
   • More properties of Fourier series coefficients
7. Parseval's theorem
   • Parseval's Theorem
   • Eigenfunctions
   • Application to infinite series
8. Discrete-time Fourier series
   • Discrete-time Fourier series
9. Fourier transform
   • Fourier transform
   • Filter design
   • Delay
10. Properties of Fourier transform
    • More Fourier transform examples
    • Partial fraction expansion
    • Properties of Fourier transform
11. Duality of Fourier transform
    • Duality of Fourier transform
    • More properties of Fourier transform
12. Aliasing and filtering
    • Aliasing
    • Filtering examples
13. Misc
    • Discrete Fourier expansion example