Fourier transforms appear when limits are applied to Fourier series, which are usually a series representation of functions on a circle. Fourier transform can best be applied to handle problems with non-periodic functions. There are a lot of ordinary and partial differential equation problems which require the knowledge of Fourier transform to simplify their solutions.
We define the Fourier transform of a piecewise continuous and absolutely integrable function by
and the inverse Fourier transform by
Here must converge.
Now, let's look at an example.
Let Compute the Fourier transform of
Solution
By definition
Note that
The generalization to high dimensions:
https://see.stanford.edu/materials/lsof ... /chap8.pdf
-
- Active Topics
-
-
- by Eli 10 hours ago Collection of Greatest Christian Hymns of all Times View the latest post Replies 34 Views 54394
- by Eli 1 day ago Pondering Big Cosmology Questions Through Lectures and Dialogues View the latest post Replies 34 Views 55945
- by Eli 1 day ago Russia Invades Ukraine View the latest post Replies 652 Views 221111
- by Eli 1 day ago Re: What is in Your Mind? View the latest post Replies 693 Views 285386
- by Eli 2 days ago Programmatically Manipulate Files: Renaming, Reading, Writing, Deleting, and Moving Files Between Folders View the latest post Replies 7 Views 3477
- by Eli 1 week ago Iran Launches Retaliatory Attack Against Israel, and Israel Retaliates by Attacking Iranian Isfahan Millitary Base View the latest post Replies 28 Views 3016
- by Eli 1 week ago All in One: YouTube, TED, X, Facebook and Instagram Reels, Videos, Images and Text Posts View the latest post Replies 319 Views 20221
- by Eli 1 week ago Python Packages for Scientific Computing View the latest post Replies 8 Views 11250
- by Eli 1 week ago Dunia Yetu: Building Tanzania's Digital Future Together View the latest post Replies 5 Views 2019
- by Eli 3 weeks ago What is Retrieval-Augmented Generation (RAG)? View the latest post Replies 2 Views 2193
-
Fourier Transform
-
- Information
-
Who is online
Users browsing this forum: No registered users and 0 guests