Need a help about Fourier Integral.

In summary, the conversation is about a student seeking help with understanding the Fourier Transform and the problem with the Fourier Integral of non-periodic functions. The other person in the conversation offers help and suggests looking for the proof in a textbook on Fourier analysis. They also ask for clarification on the definition of Fourier Integral being used.
  • #1
nnvkct
1
0
http://img96.imageshack.us/img96/4240/hinhcc9.jpg

I'm studying on Fourier Transform. And the only thing I don't understand about it still now is the problem about Fourier Integral with non-periodic function. Why we can write it in the form above ? Please help me.:cry: I appreaciate any help.

Best regard.
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
You don't have to figure that out by yourself. :smile: That stuff is a theorem that isn't easy to prove, but if you're interested you can find the proof in any textbook on Fourier analysis.
 
  • #3
First, what definition of Fourier Integral are you using? Once you have answered that we may be able to help you see how to change it to the form you want.
 

FAQ: Need a help about Fourier Integral.

1. What is a Fourier Integral?

A Fourier Integral is a mathematical tool used to decompose a complex function into its individual frequency components. It is a type of Fourier Transform that is used to represent a continuous function in terms of its frequency components.

2. How is a Fourier Integral different from a Fourier Series?

A Fourier Integral is used for continuous functions, while a Fourier Series is used for periodic functions. Additionally, a Fourier Integral can represent a function with an infinite number of frequencies, while a Fourier Series can only represent a function with a finite number of frequencies.

3. What is the importance of Fourier Integrals in science and engineering?

Fourier Integrals are essential in analyzing and understanding complex systems and phenomena in science and engineering. They are used in fields such as signal processing, image and sound analysis, and quantum mechanics.

4. How is a Fourier Integral calculated?

A Fourier Integral involves integrating a function over an interval of time or space. The integral is evaluated using a mathematical formula known as the Fourier Transform, which converts the function from the time or space domain to the frequency domain.

5. Are there any limitations to using Fourier Integrals?

One limitation of Fourier Integrals is that they cannot be used for functions that are not integrable, such as functions with infinite discontinuities or infinite oscillations. Additionally, they may not accurately represent functions with rapidly changing components or functions with a discontinuous derivative.

Similar threads

A few questions to make sure I understand Fourier series
Replies
3
Views
868
Fourier transform of exponential function
Replies
3
Views
2K
What is the Exponential Fourier Transform of an Even Function?
Replies
8
Views
1K
How to 'shift' Fourier series to match the initial condition of this PDE?
Replies
4
Views
1K
How Do You Prove the Fourier Transform Definition Using Integral Evaluation?
Replies
5
Views
1K
Using Parseval's Theorem to evaluate an integral -- Help please
Replies
1
Views
4K
Fourier Series of Sawtooth Wave from Inverse FT
Replies
2
Views
2K
Help with found Fourier complex series of e^t
Replies
1
Views
952
Why is Fourier Transform of a Real Function Complex?
Replies
5
Views
2K
Fourier Integrals and Division
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top