# How to teach mathematically about Fourier analysis and synthesis? [duplicate]

I have recently started teaching. It gets totally blank in front of the big crowd. Now, I am quite confused about how to start teaching the Fourier transform and Fourier series chapter.

I want students be convinced and motivated to learn this difficult concept .

Can anybody give mathematical explanation about

How Fourier Analysis is performed ? Can anybody give a simple example?

How Fourier Synthesis is performed ? Can anybody give a simple example ?

• The question of what is the need and why are they important has already been asked: matheducators.stackexchange.com/questions/7469/… May 17, 2015 at 8:48
• @DavidButlerUofA OK sir .I have skipped Fourier series from the question May 17, 2015 at 9:01
• General advice for beginning teachers: follow the textbook! Especially in elementary courses. Do not try to do anything different. May 17, 2015 at 13:18

## 2 Answers

You could make the connection between Fourier synthesis and (musical) synthesizers. Maybe you could play some interesting tones from a synthesizer. How do we figure out what goes into the synthesis? Fourier analysis.

A lot of students will (sadly) shut down while you're telling them things that "won't be on the test". It would help if you could repeatedly loop back to the example as you cover topics in Fourier analysis.

My opinion is that, as a teacher, you aren't responsible for "convincing" students that this is an interesting topic. You just have to teach it so that the subset of students that is actually hardworking will be able to solve the problems on the final exam.

You can give some general motivational examples from digital signal processing, but, honestly, an introductory course doesn't remotely bring students close to modern practical application along these lines.

• I down-voted because (1) you have not answered the question, and (2) you have the sentence: "You just have to teach it so that the subset of students that is actually hardworking will be able to solve the problems on the final exam." May 18, 2015 at 21:40
• @BenjaminDickman Reason (1) is fair enough I suppose. May 19, 2015 at 2:25