[2026 July 14] Fast Fourier Transform (FFT) for Engineers in the Making

Undergraduate course, The University of Queensland, School of Electrical Engineering and Computer Science, 2026

I’m a lecturer of ELEC3100: Fundamental of EM waves and fields (aka. time-varying fields) since 2024.

This can be used as a 25-to-30 min FFT lecture, with optional usage of matrix-form of FFT with another 5-to-10 min.

You need to assume your students at least see the form of Fourier Integral before in 2nd year in Australia or 1st year in some other countries.

Why this FFT Lecture:

Most students and professional engineers may just call one line command of FFT in real life after the course.
Most people don’t care all boring math behind it.
I propose, here is way to explain and convince engineers in the making (students) to learn FFT in a light way
Everyone know how boring FFT can be, below in Textbook section and Online materials, you are welcome to learn in the hard way if you want.
I always prefer to learn a new thing in a light way step by step and directly tell me why it is useful as my math is not good (compared a majority of genius in the rest of the world).
As I really do not care math solely, there are plenty of 1980s math and physics I have learnt yet, but didn’t impact my life.

(Really, in reality, most engineering students will “fall asleep” and are not able to digest FFT complicated math in the typical way we taught them.

Lecturers may also choose to skip assessing how FFT really work in final exam, as student evaluation survey plays the role.)

What is covered (the logic)

(p.3 to p.7): Why we need Fourier Transform and its usage in real world which is FFT
(p.8 - p.9): What is Fast Fourier Transform
(p.10): Why FFT is called “Fast” Fourier Transform
(p.11): When “Fast Fourier Transform” can be slow?
(p.11, p.12): A trick called zero padding
(p.13): FFT can be wrong, how to sample the signal properly as an engineer?
(p.14 to p.16): 1D and 2D FFT applications (audio and image processing)
(p.17 - p.19): FFTshift we encountered in 1D and 2D FFTapplications when we really code it up
(p.22 - p.29): How does the FFT algorithm work (with a 2-point and 4-point FFT example)?
[Optional] (p.32 - p.36): the generic matrix-form of FFT with 4-point FFT example