## Contents

- 1 This pages contains exercises to practice computing the Fourier series of a DT signal
- 1.1 Recall the basic formulas
- 1.2 Case 1: For some periodic functions, the Fourier series coefficients must be obtained using the above summation formula
- 1.3 Case 2: Some periodic functions (e.g. sine and cosine) can be directly expanded into a linear combination of complex exponentials
- 1.4 Questions

# This pages contains exercises to practice computing the Fourier series of a DT signal

Note: This is a collective study page. You are expected to participate by adding content/comment/questions/exercises etc. This is a wiki after all!

## Recall the basic formulas

- Fourier series of a discrete-time signal x[n] periodic with period N

- $ x[n]=\sum_{k=0}^{N-1} a_k e^{j \frac{2\pi}{N}kn} $

- Fourier series coefficients of a continuous-time signal x(t) periodic with period T

- $ a_k=\frac{1}{N} \sum_{0}^{N-1} x[n] e^{-j \frac{2\pi}{N}nk} $

## Case 1: For some periodic functions, the Fourier series coefficients must be obtained using the above summation formula

- DT Fourier series coefficients of a periodic square wave (in DT)
- add your own example here
- add your own example here

The following pages contain a periodic signal along with a computation of the Fourier series coefficients of that signal. These were contributed by your peers in ECE301. Check whether the answers are correct. Are all the steps explained clearly and logically? Do you have questions? Feel free to comment directly on the pages!

## Case 2: Some periodic functions (e.g. sine and cosine) can be directly expanded into a linear combination of complex exponentials

The following pages contain a periodic signal along with a computation of the Fourier series coefficients of that signal. These were contributed by your peers in ECE301. Check whether the answers are correct. Are all the steps explained clearly and logically? Do you have questions? Feel free to comment directly on the pages!

- HW4.1_Caleb_Tan_ECE301Fall2008mboutin
- HW4.2_Eric_Zarowny_ECE301Fall2008mboutin
- HW4.2_Wei_Jian_Chan_ECE301Fall2008mboutin Interesting and common mistake here!
- See more exercise in the second question of this page

## Questions

- What is the difference between the Fourier series of a signal, and the Fourier series coefficients for a signal?
- Answer here