FOURIER ANALYSIS

By Joshua Tanner and Ronald Doung

Math 320

3/15/10

Types of Waves

Slinky Wave

Interference

Constructive Destructive

Analog to Digital

The Nyquist limits – Making sure you have enough points to show the wave.

Analog waves and Digital Waves

Waves and Numbers

Who is Fourier Jean Baptiste Joseph Fourier,

1768 - 1830 He was a French mathematician

and physicist during the reign of emperor Napoleon

In 1822 he published the Théorie analytique de la chaleur

His work claimed that any periodic function f(x) can be expressed as a series of sine functions

Fourier transformations, Fourier series and Fourier analysis was later named in his honor

What is Fourier Analysis?

Given any periodic function, a function can be written as a sum of trigonometric functions

This idea is based on prior knowledge of constructive and destructive interference

Basic idea: “taking the limit of the sum of the trig functions to infinity will produce the desired graph”

Fourier Analysis in the Real World Fourier analysis and transformations have many

applications in the real world. Some of these include:

Touch-tone dialingThe dialing pad acts as a matrix, each key

corresponds to two frequencies Sound editing

Given an audio recording, we can separate unwanted sound frequencies from initial recording

Image processingCan remove unwanted wave patterns from radio

frequency caught by a digital camera