1. By Joshua Tanner and Ronald Doung Math 320 3/15/10
Fourier Analysis
By Joshua Tanner and Ronald Doung
Math 320
3/15/10

2. Types of Waves

3. Slinky Wave

4. Interference
Constructive
Destructive

5. Analog waves and Digital Waves
Analog to Digital
Analog waves and Digital Waves
The Nyquist limits – Making sure you have enough points to show the wave.

6. Waves and Numbers

7. 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

8. 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”

10. Fourier Analysis in the Real World
Fourier analysis and transformations have many applications in the real world. Some of these include:
Touch-tone dialing
The 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 processing
Can remove unwanted wave patterns from radio frequency caught by a digital camera