## Stanford Engineering Everywhere EE261 - The Fourier Transform and its Applications

author: Brad G. Osgood,
Computer Science Department, Stanford University

released under terms of: Creative Commons Attribution Non-Commercial (CC-BY-NC)

released under terms of: Creative Commons Attribution Non-Commercial (CC-BY-NC)

The goals for the course are to gain a facility with using the Fourier transform, both specific techniques and general principles, and learning to recognize when, why, and how it is used. Together with a great variety, the subject also has a great coherence, and the hope is students come to appreciate both.

Topics include:

- The Fourier transform as a tool for solving physical problems.
- Fourier series, the Fourier transform of continuous and discrete signals and its properties.
- The Dirac delta, distributions, and generalized transforms.
- Convolutions and correlations and applications; probability distributions, sampling theory, filters, and analysis of linear systems.
- The discrete Fourier transform and the FFT algorithm.
- Multidimensional Fourier transform and use in imaging.
- Further applications to optics, crystallography.
- Emphasis is on relating the theoretical principles to solving practical engineering and science problems.

**Course Homepage:** http://see.stanford.edu/see/courseinfo.aspx?coll=84d174c2-d74f-493d-92ae-c3f45c0ee091

**Course features at Stanford Engineering Everywhere page:**

Woldegebriel Assefa, June 19, 2011 at 10:47 a.m.:I am from Ethiopia. I have I got the You tube lecture very interesting. I would be very happy if I get the materials for this course( Fourier transforms) in soft copy and/or hard copy. please, if possible, can you send me the handouts through the mailing address:

To

Woldegebriel Assefa

Mekelle University

P.o.box 3162

Mekelle-Ethiopia

vp singh, January 26, 2012 at 12:57 p.m.:Sir, I just gone through the EE261 'The Fourier Transform and its application' as I was preparing my son for engineering exam for electronic and comuniciation. The applied math has been beautifully embedded in practice and signals .

Dr Justin Whitty, June 3, 2015 at 10:18 a.m.:Hi Prof,

Just like to thank you for an amazing on line course. I viewed all of your lectures a couple of years ago and I was simply amazed by the level of detail but more importantly the ease in which you get across some of the really nice nuances of the subject matter. I finally have a working knowledge of the Theory of Distributions and kind of now get what cheating convolution is all about. Best bit for me is really really elegant proof of the convolution theorem.

I have now embedded your brilliant lectures in to a few of the post-graduate courses at the University of Central Lancashire in the UK.

I just wish I could teach as well as you do on this course it is a joy to watch you in action dear fellow.

I have also completed (well cheated a lot of the time using the MAXIMA CAS) your problem sets. I had load of fun scratching my mathematical head a number of times on quite a few of these. Therefore has a great sense of Joy when I finally (well MAXIMA) solved them.

Dare I say, Pure Genius.....

Very best wishes,

Justin

Qubus, February 1, 2016 at 4:01 p.m.:Having given a course that involved similar topics, I can say "an excellent set of lectures". What an amazing speed you can write at! The oral delivery is a bit on the fast side though. I imagine that that makes it rather difficult for non-native English speakers.

Also an improvement could be made in the videos, if the camera were a bit more agile, always showing what has just been written on the board.

On the whole, extremely good.

Congratulations.

Michael, May 30, 2016 at 5:19 a.m.:Excellent along with your text "The Fourier Transform and its Applications"

Dr.Thomas Kuruvilla, March 31, 2017 at 2:53 p.m.:I am from southern part of India. Professor Osgood explaining every aspect Fourier transform so that it is useful to students from all branches of science and technology .

Providing the text will greatly benefit the non english speaking students much.

Where can we get the Matlab codes?