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

Types of Waves

Slinky Wave

Interference Constructive Destructive

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.

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 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