Fourier Series
Introduction
Periodic function
Frequency, Angular frequency
and Amplitude
1
𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 =
𝑃𝑒𝑟𝑖𝑜𝑑
2𝜋
𝐴𝑛𝑔𝑢𝑙𝑎𝑟 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 = 2𝜋 × 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐 =
𝑃𝑒𝑟𝑖𝑜𝑑
Amplitude is the maximum displacement or
distance moved by a point on a vibrating body or
wave measured from its equilibrium position
Example 1
Period:
Frequency:
Angular Frequency:
Amplitude:
Example 2
Period:
Frequency:
Angular Frequency:
Amplitude:
Exercise 1
Question 1
Question 2
Even and Odd Function
Definition:
Even function symmetry about the y
axis and odd function symmetry around
the origin
Integrating odd function over
symmetric domain
Integrating even function over
symmetric domain
Fourier Series
Fourier Series
Fourier Coefficient for even functions
Fourier Coefficient for odd functions
Example 3
Example 4
Example 5