1. Jean Baptiste “Joseph Fourier” By Muhammed Al-walker

2. Early Life  Born March 1768 in Auxeme Bourgogne France  Father was a tailor his mother was his Father’s second wife  9th child out of 12 kids  Going into school He showed much promise at the young age of 13  He learned Latin and French

3. Life Continued  He Went to school to become a priest  But He also was apart of the French revolution and Napoleon’s Expedition  He was apart of Napoleons army as its scientific advisor  While on the exposition with napoleon; Napoleon, Him, and others Founded the Cairo Institute.  He was also a founding member of the math department there

4. Education  When he got older he became a teacher at Benedictine college  He was renowned as an outstanding lecturer at College de France  Professor of Analysis at the École Polytechnique.  In 1790 He became a teacher at Benedictine college in math  After the French Revolution he began teaching at College de France  He began his mathematical research there with Lagrange, Laplace, and Monge  It was during his time in Grenoble that Fourier did his important mathematical work on the theory of heat

5. Fourier Theory of Heat  Fourier was interested in the way heat flowed inside and around materials, and in the process of studying this phenomenon he derived his transform  He Could have never known how much his theory would effect Modern technology, music, science, and engineering were  With his theory of heat he opened the way for The Fourier Series,analysis, and transform theories

6. Fourier Series  By definition it is an Infinite Series of Trigonometric functions that represent an expansion or approximation of a periodic function

7. Fourier Analysis  The process of decomposing a musical instrument sound or any other periodic function into its constituent sine or cosine waves is called Fourier analysis. You can characterize the sound wave in terms of the amplitudes of the constituent sine waves which make it up.

8. Fourier Transform  a function derived from a given function and representing it by a series of sinusoidal functions.  Fourier Transform provides the music you stream every day, squeezing down the images you see on the Internet into tiny little JPG files, and even powering your noise-canceling headphones. Here’s how it works.  The equation owes its power to the way that it lets mathematicians quickly understand the frequency content of any kind of signal.

9. From Math To Music  Sound waves are one type of waves that can be analyzed using Fourier series and transform, allowing for different aspects of music to be analyzed using this method.  Musical instruments produce sound as a result of the vibration of a physical object such as a string on a violin, guitar, or piano, or a column of air in a brass or woodwind instrument. This vibration causes a periodic variation in air pressure that is heard as sound.

10. Cont.  His major breakthrough was realizing that complicated signals could be represented by simply adding up a series of far simpler ones. He chose to do it by adding together sinusoids  Say you strike a chord on a piano by pressing three keys. You can produce three different notes, with well defined frequencies  They look like nice friendly sine waves but combine them and you make a final sound wave a brand new sound in itself  It looks complicated, but we know that fundamentally it’s just three plain sine waves staggered in time and added together

11. End Note  Todays music thrives on these theory's  Without them we wouldn’t have iPod’s, headphones, or even music videos