An introduction to the "systems" approach to solving physical problems: the delta function, impulse response, transfer functions, the Fourier transform, sampling and the FFT, causality and the Kramers-Kronig relations, noise processes and matched filtering.
You have reached the course support page for PHSI 427 in 2024, formerly known as ELEC 441 - Linear Systems and Noise (pre-2023).
Lecturer
Lecture times and room
Workshop
Assessment
Text
Assignments
If you want to have a look at the assignments from 2023, here they are: Assignment 1, Assignment 2, Assignment 3, Assignment 4, Assignment 5, Assignment 6.
Workshops
Lecture content (sections are in the 2021 course notes; topics and timing will change a bit as we go along in 2024)
| Lecture | Date | Sections | Content | |
|---|---|---|---|---|
| 1 | 29 Feb (9) | 1.1, 1.2 | delta function = Dirac delta function = unit impulse | scan |
| 2 | 29 Feb (10) | 2.1-2.5 | Classes of systems. Impulse response, convolution | scan |
| 3 | 7 Mar (9) | 2.7-2.9 | Stability of LTI system, eigenfunctions of LTI systems, transfer function, cascaded systems | scan |
| 4 | 7 Mar (10) | 3.1-3.3, 3.5 | The Fourier transform and its inverse. Convergence of Dirichlet integrals. Properties of FT. | scan |
| 5 | 14 Mar (9) | 3.3 | Symmetries and convolution theorem. | scan |
| 6 | 14 Mar (10) | 3.4 | Examples of FT | scan |
| 7 | 21 Mar (9) | 3.6, 3.7 | FT of generalized functions | |
| 8 | 21 Mar (10) | 4.1-4.7 | Sampling in frequency and time, Discrete-time FT, Sampling theorem | |
| 9 | 28 Mar (9) | 5.1, 5.4 | Discrete FT | |
| 10 | 28 Mar (10) | 5.4-5.5 | Properties of the DFT, Fast Fourier transform (FFT) | |
| 11 | 11 Apr (9) | 6.1, 6.2 | Energy and power in deterministic signals | |
| 12 | 11 Apr (10) | 6.3, 6.4 | Probability, A CLT | |
| 13 | 18 Apr (9) | |||
| 14 | 18 Apr (10) | 7.5,7.6 | Stochastic processes, wide-sense stationary | |
| 15 | 2 May (9) | 8.1, 8.2, 9.10 | Power in stochastic signals, the real Wiener--Khinchin theorem | |
| 16 | 2~May~(10) | Overflow |
Exam prep