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 18 hours ago Re: What is in Your Mind? View the latest post Replies 703 Views 299832
- by Eli 18 hours ago Russia Invades Ukraine View the latest post Replies 663 Views 234993
- by Eli 2 days ago All in One: YouTube, TED, X, Facebook and Instagram Reels, Videos, Images and Text Posts View the latest post Replies 326 Views 34033
- by Eli 3 days ago PySpark for Large Data Processing View the latest post Replies 1 Views 6860
- by Eli 1 week ago President Museveni's Speech During International Development Association (IDA) Summit View the latest post Replies 1 Views 280
- by Eli 1 week ago From Simple Linear Regression Analysis to Covariance & Correlation to Independent Determinant, and R-Squared View the latest post Replies 11 Views 24833
- by Eli 1 week ago Collection of Greatest Christian Hymns of all Times View the latest post Replies 34 Views 67201
- by Eli 1 week ago Pondering Big Cosmology Questions Through Lectures and Dialogues View the latest post Replies 34 Views 58068
- by Eli 1 week ago Programmatically Manipulate Files: Renaming, Reading, Writing, Deleting, and Moving Files Between Folders View the latest post Replies 7 Views 15611
- by Eli 2 weeks ago Iran Launches Retaliatory Attack Against Israel, and Israel Retaliates by Attacking Iranian Isfahan Millitary Base View the latest post Replies 28 Views 17633
-
Fourier Transform
-
- Information
-
Who is online
Users browsing this forum: No registered users and 1 guest