Understanding Fourier Series: Solving a Tricky Question with Step-by-Step Guide

In summary, a Fourier series is a mathematical representation of a periodic function as a sum of sine and cosine functions. It is used in many applications such as signal processing, image and sound compression, and solving differential equations. To calculate a Fourier series, coefficients of sine and cosine functions are found using Fourier analysis. A Fourier series differs from a Fourier transform in that it deals with periodic functions while a Fourier transform deals with non-periodic functions. Fourier series are widely used in real-life applications, particularly in digital signal processing and understanding physical phenomena such as sound and electromagnetic waves.
  • #1
VooDoo
59
0
hey guys,

I got this question that I am a bit stuck on. I have done question two and got the Fourier series, but have no idea how to do part 3. Any help is very appreciated.
http://img453.imageshack.us/img453/5103/file2yp2.jpg
 
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  • #2
What did you get for exercise 2? That will probably be quite useful information for solving 3!
 
  • #3
Hi, I got the following for my Fourier series. I have a 1/n^2 term in there which looks good.
http://img392.imageshack.us/img392/5124/11111je7.jpg
 
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  • #4
Choose an appropriate x.
 

FAQ: Understanding Fourier Series: Solving a Tricky Question with Step-by-Step Guide

What is a Fourier series?

A Fourier series is a mathematical representation of a periodic function as a sum of sine and cosine functions. It is used to analyze and approximate periodic signals and is an important tool in signal processing, harmonic analysis, and differential equations.

What are the applications of Fourier series?

Fourier series have a wide range of applications in various fields such as physics, engineering, mathematics, and computer science. Some common applications include signal processing, image and sound compression, solving differential equations, and analyzing vibrations and waves.

How is a Fourier series calculated?

A Fourier series can be calculated by finding the coefficients of the sine and cosine functions that best fit the given periodic function. This is done using a mathematical technique called Fourier analysis, which involves integrating the function over a period and solving for the coefficients.

What is the difference between a Fourier series and a Fourier transform?

A Fourier series deals with periodic functions while a Fourier transform deals with non-periodic functions. A Fourier series decomposes a periodic function into a sum of sine and cosine functions, while a Fourier transform decomposes a non-periodic function into a sum of complex exponential functions.

Are Fourier series used in real-life applications?

Yes, Fourier series are used extensively in real-life applications such as in digital signal processing, image and sound compression, and solving differential equations. They are also used in analyzing and understanding various physical phenomena such as sound waves, electromagnetic waves, and vibrations.

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