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