PHSI 427: Linear Systems and Noise

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 2025, formerly known as ELEC 441 - Linear Systems and Noise (pre-2023).

Lecturer

Colin Fox. Room 523. colin.fox@otago.ac.nz

Lecture times and room

Thursday 3:00pm - 4.50pm, room 311 (with a tea break 3:50 to 4:00) for weeks 1-6 (university weeks 9-15), then 1.5 weeks after the mid-semester break (university weeks 18-19) of semester 1 in 2025. That is, 8.5 weeks of lectures, starting in the first week, with a gap for the week before mid-semester break and the week of mid-semester break.

Workshop

Monday 11am - 11.50am, 311

Assessment

30% assignments, 70% exam (3 hours, closed book)

Text

We will be using the 2025 edition of the study notes Δ by Tan & Fox.

The classic text by Ron Bracewell: The Fourier Transform & Its Applications is well worth a read, if only for the pictionary of transforms, but it is a bit out of date and very expensive to buy.

Assignments

There will be 6 weekly assignments (set weeks 1-6, due weeks 2-7), worth 5% each. Assignments are made available immediately after the Thursday lecture, and are due 3pm the following Thursday.
Assignment 1 Δ, Assignment 2 Δ, Assignment 3 Δ, Assignment 4 Δ, Assignment 5 Δ, Assignment 6 Δ

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

Monday workshops are firstly for sorting out issues relating to assignments, after that we will go over some workshop question sheets: The sheets from 2023 are (we will probably reuse these in 2025): Workshop 1, Workshop 2, Workshop 3.

Lecture content (sections are in the 2024 course notes; topics and timing might change a bit as we go along in 2025)

Lecture	Date	Sections	Content
1	27 Feb (3pm)	1.1, 1.2	delta function = Dirac delta function = unit impulse	scan Δ
2	27 Feb (4pm)	2.1-2.5	Classes of systems. Impulse response, convolution	scan Δ
3	6 Mar (3pm)	2.7-2.9	Stability of LTI system, eigenfunctions of LTI systems, transfer function, cascaded systems	scan Δ
4	6 Mar (4pm)	3.1-3.3, 3.5	The Fourier transform and its inverse. Convergence of Dirichlet integrals. Properties of FT.	scan Δ
5	13 Mar (3pm)	3.3	Symmetries and convolution theorem.	scan Δ
6	13 Mar (4pm)	3.4	Examples of FT	scan Δ
7	20 Mar (3pm)	3.6, 3.7	FT of generalized functions
8	20 Mar (4pm)	4.1-4.7	Sampling in frequency and time, Discrete-time FT, Sampling theorem
9	27 Mar (3pm)	5.1, 5.4	Discrete FT
10	27 Mar (4pm)	5.4-5.5	Properties of the DFT, Fast Fourier transform (FFT)
11	10 Apr (3pm)	6.1, 6.2	Energy and power in deterministic signals
12	10 Apr (4pm)	6.3, 6.4	Probability, A CLT
13	1 May (3pm)
14	1 May (4pm)	7.5,7.6	Stochastic processes, wide-sense stationary
15	8 May (3pm)	8.1, 8.2, 9.10	Power in stochastic signals, the real Wiener--Khinchin theorem
16	8~May~(4pm)		Overflow

Exam prep

A collection of past exams can be found here or on the Otago library site and search for ELEC441. Post 2013 are most relevant. Here is a booklet of old exam questions (2002 -- 2008).