answersLogoWhite

0

Still curious? Ask our experts.

Chat with our AI personalities

SteveSteve
Knowledge is a journey, you know? We'll get there.
Chat with Steve
BeauBeau
You're doing better than you think!
Chat with Beau
LaoLao
The path is yours to walk; I am only here to hold up a mirror.
Chat with Lao

Add your answer:

Earn +20 pts
Q: What is the importance of Fourier transforms?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Continue Learning about Math & Arithmetic

Can you give an example of how Fast Fourier Transforms are used in financial models?

There is a beautiful paper by Ales Cerny entitled "Introduction to Fast Fourier Transform in finance", which gives many interesting examples.


How does the graph of Fourier Series differ to the graph of Fourier Transform?

You can graph both with Energy on the y-axis and frequency on the x. Such a frequency domain graph of a fourier series will be discrete with a finite number of values corresponding to the coefficients a0, a1, a2, ...., b1, b2,... Also, the fourier series will have a limited domain corresponding to the longest period of your original function. A fourier transforms turns a sum into an integral and as such is a continuous function (with uncountably many values) over the entire domain (-inf,inf). Because the frequency domain is unrestricted, fourier transforms can be used to model nonperiodic functions as well while fourier series only work on periodic ones. Series: discrete, limited domain Transform: continuous, infinite domain.


What is the difference between Fourier transform and Laplace transform and z transform?

Fourier transform and Laplace transform are similar. Laplace transforms map a function to a new function on the complex plane, while Fourier maps a function to a new function on the real line. You can view Fourier as the Laplace transform on the circle, that is |z|=1. z transform is the discrete version of Laplace transform.


What did Joseph fourier discover?

Joseph Fourier is a French mathematician and physicist. Fourier is generally credited with the discovery of the greenhouse effect.


What is the difference between fourier series and discrete fourier transform?

Fourier series is the sum of sinusoids representing the given function which has to be analysed whereas discrete fourier transform is a function which we get when summation is done.