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 4 minutes ago Pondering Big Cosmology Questions Through Lectures and Dialogues View the latest post Replies 34 Views 55022
- by Eli 23 minutes ago Russia Invades Ukraine View the latest post Replies 652 Views 220178
- by Eli 34 minutes ago Re: What is in Your Mind? View the latest post Replies 693 Views 284338
- by Eli 1 day ago Programmatically Manipulate Files: Renaming, Reading, Writing, Deleting, and Moving Files Between Folders View the latest post Replies 7 Views 2581
- by Eli 6 days ago Iran Launches Retaliatory Attack Against Israel, and Israel Retaliates by Attacking Iranian Isfahan Millitary Base View the latest post Replies 28 Views 2150
- 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 19221
- by Eli 1 week ago Python Packages for Scientific Computing View the latest post Replies 8 Views 11225
- by Eli 1 week ago Dunia Yetu: Building Tanzania's Digital Future Together View the latest post Replies 5 Views 1988
- by Eli 2 weeks ago Collection of Greatest Christian Hymns of all Times View the latest post Replies 33 Views 53470
- by Eli 3 weeks ago What is Retrieval-Augmented Generation (RAG)? View the latest post Replies 2 Views 1364
-
Fourier Transform
-
- Information
-
Who is online
Users browsing this forum: No registered users and 0 guests