Could someone explain Fourier series and Fourier transform in understandable language for me?

Question

hey guys, i have to do math IV for my bachelors next year and im doing the math im gona have to do to catch up and get a headstart so i know sort of what to do next year. but...
they do complex fourier transforms and fourier series but i couldnt remember how to do it or what it is and how it works. ive googled on the net "easy fourier series tutorials" but i get all these people who talk in "high mathematical language" and its hard to get what they mean. (english is my second language)

does anyone know of a site that teaches math like that in an understandable language meaning using standard terms and examples without bombarding me with all these fancy terms and stuff? im not stupid i just dont get it. i have math background from my electronic engineering diploma days but now two years later i wana start with my bachelors. im a bit rusted on the math but i catch up quickly.
any suggestions please??
thanks alot

Answer 1

The idea is that any "function" can be viewed as a "signal" -- you can think of the independent variable x as the time, and the function f(x) as the signal at any given time.



Then what you do is break down the function in terms of frequencies. Any reasonable signal can be though of as, basically, a "sound" signal -- and all sounds are composed of frequencies.



So the Fourier series takes f(x) and transforms it into F(q) where F(q) tells you the strength of each frequency q in the signal f(x).



The mathematics of integration (calculus) tell you how to break down the signal and compute the frequencies. You can then decompose f(x) into its components of each frequency.



I hope that I have been able to explain this in plain language, without any confusing equations or symbols or anything -- those are important, but you can't learn them without understanding what it means, and hopefully the explanation I've given will help you with that. To start working on the technicals, I suggest MIT's open courses, or try reading Wikipedia (it can be helpful for a topic like Fourier series).

Answer 2

B.S. Grewal is a stable e book whilst it is composed of series (convergency, divergency, fourier etc). inspite of the undeniable fact that it unquestionably sucks in all different fields. additionally, fourier transforms at the instant are not coated. i'm uncertain if the subject count is provided in bigger engineering arithmetic by Kreyzsig, verify as quickly as. you additionally can use the video clips created by NPTEL. you will discover them on youtube.

Answer 3

Paul's Online Notes is a good reference for Calc I-III and Intro to DEs. I think he's a teacher, so the notes are relatively easy to follow. He covers Fourier series in the DE section.



http://tutorial.math.lamar.edu/Classes/DE/FourierSineSeries.aspx



When we covered Fourier series in my DE class, we barely scratched the surface. We didn't really work with them until I took an Instrumentation & Measurements course. The textbook was Theory and Design for Mechanical Measurements, and it did a much better job explaining than the math book. So check you old engineering textbooks.



Also MIT has information from some of their courses online. I've posted a link to a DE class where you can get course notes and video lectures: http://ocw.mit.edu/OcwWeb/Mathematics/18-03Spring-2006/CourseHome/index.htm



This may help as well:

http://ocw.mit.edu/ans7870/18/18.013a/textbook/HTML/chapter30/section08.html