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 3 hours ago Chat With ChatGPT - An Interactive Conversational AI View the latest post Replies 21 Views 22789
- by Eli 8 hours ago All in One: YouTube, TED, X, Facebook and Instagram Reels, Videos, Images and Text Posts View the latest post Replies 283 Views 6610
- by Eli 10 hours ago CAF Champions League Quarter Finals: Simba vs Al Ahyl View the latest post Replies 1 Views 32
- by Eli 1 day ago Russia Invades Ukraine View the latest post Replies 643 Views 209081
- by Eli 1 day ago Collection of Greatest Christian Hymns of all Times View the latest post Replies 30 Views 42713
- by Eli 6 days ago Re: What is in Your Mind? View the latest post Replies 658 Views 271431
- by Eli 1 week ago Mission Control Live: NASA InSight Mars Landing Live Coverage View the latest post Replies 32 Views 12975
- by Eli 1 week ago Christian Podcasts View the latest post Replies 4 Views 28285
- by Eli 1 week ago Python Packages for Scientific Computing View the latest post Replies 7 Views 2715
- by Eli 1 week ago Pondering Big Cosmology Questions Through Lectures and Dialogues View the latest post Replies 32 Views 44770
-
Fourier Transform
-
- Information
-
Who is online
Users browsing this forum: No registered users and 0 guests