1 / 10

Fourier Analysis

By Joshua Tanner and Ronald Doung Math 320 3/15/10. Fourier Analysis. Types of Waves. Slinky Wave. Interference. Constructive. Destructive. Analog to Digital. Analog waves and Digital Waves. The N yquist limits – Making sure you have enough points to show the wave. Waves and Numbers.

lexine
Download Presentation

Fourier Analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

  2. Types of Waves

  3. Slinky Wave

  4. Interference Constructive Destructive

  5. 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 Théorieanalytique 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”

  9. 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

More Related