How Do You Compute the Fourier Series for |sin(x)| Over the Interval (-1,1)?

In summary, the conversation discusses finding the Fourier series of the function f(x)=|sin(x)| on the interval (-1,1). There is confusion about whether to integrate from -1 to 1 or consider a period of pi or 2. The person has emailed their instructor for clarification.
  • #1
Dassinia
144
0
Hello,
Find the Fourier serie of f(x)=|sin(x)| on the interval (-1,1)

I'm just a little confused, does that mean that I have to integrate from -1 to 1 to find the coefficients ? Because the formula of the coefficients is in terms of the period T, for this function the period is pi. Or do I have to consider it only in -1,1 and take the period T=2 ?

Thanks
 
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  • #2
For a homework problem, it seems like the given interval might be a typo or the function was supposed to be ##\lvert \sin \pi x \rvert##; however, there's no real reason the interval couldn't be (-1, 1) for the given function. I'd check with your instructor if I were you.
 
  • #3
It's not a homework, it's an exercise in a previous exam..
the exam is tomorrow and I just saw this exercise.. :frown:

EDIT: I sent an email to an instructor, and I had my answer !
 
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FAQ: How Do You Compute the Fourier Series for |sin(x)| Over the Interval (-1,1)?

What is a Fourier series?

A Fourier series is a mathematical representation of a periodic function as a sum of sine and cosine functions with different frequencies and amplitudes. It is used to analyze and approximate periodic signals, such as sound waves or electrical signals.

How is a Fourier series calculated?

A Fourier series is calculated using a mathematical formula called the Fourier series formula, which involves integrating the periodic function over a specific interval. This formula takes into account the different frequencies and amplitudes of the sine and cosine functions to create an accurate representation of the original function.

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

A Fourier series is a representation of a periodic function, while a Fourier transform is a representation of a non-periodic function. In other words, a Fourier series can only be used for functions that repeat over a specific interval, while a Fourier transform can be used for any function.

What are the applications of Fourier series?

Fourier series have many applications in various fields, such as signal processing, image and sound compression, and data analysis. They are also used in solving differential equations and in the study of vibrations and waves.

Are there any limitations to using Fourier series?

One limitation of using Fourier series is that it can only approximate periodic functions, so it may not be suitable for representing non-periodic signals accurately. Additionally, the convergence of a Fourier series can be affected by the discontinuities or sharp changes in a function, making it less accurate in those cases.

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