### Introduction

In this Section we examine how to obtain Fourier series of periodic functions which are either even or odd . We show that the Fourier series for such functions is considerably easier to obtain as, if the signal is even only cosines are involved whereas if the signal is odd then only sines are involved. We also show that if a signal reverses after half a period then the Fourier series will only contain odd harmonics.

#### Prerequisites

• know how to obtain a Fourier series
• be able to integrate functions involving sinusoids
• have knowledge of integration by parts

#### Learning Outcomes

• determine if a function is even or odd or neither
• easily calculate Fourier coefficients of even or odd functions