Transcript Jean Baptiste *Joseph Fourier*

Jean Baptiste “Joseph
Fourier”
By Muhammed Al-walker
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
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
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
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
Fourier Series
By definition it is an Infinite Series of
Trigonometric functions that represent an
expansion or approximation of a periodic
function
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.
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.
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.
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
End Note
 Todays music thrives on these theory's
 Without them we wouldn’t have iPod’s, headphones, or even music videos