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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.

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Fourier Analysis

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  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

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