Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

Fourier Transforms


Date: 04/20/97 at 01:18:21
From: Tracey
Subject: Fourier Transforms

Dear Dr. Math,

I am having great trouble understanding the relationship between 
Fourier transforms, Laplacian equations, and why we are always 
converting them to Z tranforms.  Why is it useful to be in the 
frequency domain rather than in the time domain?

Yours faithfully,
Tracey (A confused 6th grader)


Date: 04/20/97 at 06:22:22
From: Doctor Mitteldorf
Subject: Re: Fourier Transforms

Dear Tracey,
    
It's not every day that we get a question about Fourier transforms 
from a 6th grade student, so I don't know where to begin.  I guess 
I'll just assume you know a whole lot and ask you to slow me down if 
I'm assuming too much.
    
Fourier transforms have a world of applications, some of them in 
expected ways and some in very unexpected ways. I'm a physicist, so 
the physics applications come most easily to mind for me.
   
An example of an "expected" application is to derive the musical 
pitches making up a sound from the sound signal itself. You can find 
the overtones in a musical note, or separate the notes in a chord 
played by an orchestra, or even analyze the sound of speech to 
distinguish various phonemes (consonant and vowel sounds.)
   
An example of a "less expected" application is the solution of 
differential equations. There are many differential equations that 
are difficult to solve in the time domain, but if you just transform 
them to the frequency domain they become very easy.
   
An example of a "completely unexpected" application is quantum 
mechanics. A "wave equation" is a standard quantum mechanical 
equation for the probability of a particle being at any location 
(x,y,z) in space. If you take the Fourier transform of the function 
that solves that equation, you end up with another function that 
relates to the probability that the same particle will have any given 
momentum!
    
This is just a tiny sampling of the applications of Fourier 
transforms.  Whole books have been written on the subject.

-Doctor Mitteldorf,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Physics/Chemistry

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/