Fourier series

Mathematics for Materials and Design

The full set of notes for this topic is here. All materials on this topic can be downloaded here.

Sessions:

1. Introduction to Fourier series
   • Lecture materials: slides and handout. The MATLAB analysis demonstrated in the lecture can be accessed as a printable PDF or as a Live Script.
   • Additional materials: demonstrations of using MATLAB to analyse a square wave as a printable PDF and Live Script, and similarly for a sawtooth wave - printable PDF and Live Script.
   • Videos:
     • Introduction.
     • Piecewise and step functions.
     • Example of calculating Fourier series using MATLAB.
     • Arbitrary limits.


2. Calculating the Fourier series of functions with arbitrary period by hand
   • Lecture materials: slides and handout.
   • Videos:
     • Introduction.
     • Odd and even functions.
     • Calculating Fourier series by hand - example I.
     • Calculating Fourier series by hand - example II.


3. The Fourier transform for discrete data
   • Lecture materials: slides and handout. The MATLAB analysis demonstrated in the lecture can be accessed as a printable PDF or as a Live Script.
   • Videos:
     • Introduction and Fourier analysis.
     • Walkthrough - Fourier analysis of a discrete data set in MATLAB.