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 20 hours ago President Museveni's Speech During International Development Association (IDA) Summit View the latest post Replies 1 Views 54
- by Eli 21 hours ago From Simple Linear Regression Analysis to Covariance & Correlation to Independent Determinant, and R-Squared View the latest post Replies 11 Views 24352
- by Eli 1 day ago All in One: YouTube, TED, X, Facebook and Instagram Reels, Videos, Images and Text Posts View the latest post Replies 323 Views 24575
- by Eli 2 days ago Re: What is in Your Mind? View the latest post Replies 697 Views 289773
- by Eli 3 days ago Russia Invades Ukraine View the latest post Replies 655 Views 225452
- by Eli 3 days ago Collection of Greatest Christian Hymns of all Times View the latest post Replies 34 Views 58383
- by Eli 4 days ago Pondering Big Cosmology Questions Through Lectures and Dialogues View the latest post Replies 34 Views 57626
- by Eli 5 days ago Programmatically Manipulate Files: Renaming, Reading, Writing, Deleting, and Moving Files Between Folders View the latest post Replies 7 Views 7387
- 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 6987
- by Eli 2 weeks ago Python Packages for Scientific Computing View the latest post Replies 8 Views 13563
-
Fourier Transform
-
- Information
-
Who is online
Users browsing this forum: No registered users and 0 guests