Sample Exam Fourier Series & reverse engineering the question

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SUMMARY

The discussion centers on the properties of Fourier series, specifically regarding a series that contains only sine functions, which confirms it as an odd function. The user inquires about calculating the period of the function and the feasibility of drawing a "deleted diagram" from the Fourier series. A response clarifies that the absence of cosine terms indicates the An coefficient is zero, and suggests that the function may need to integrate to zero over the specified interval to satisfy the conditions of the Fourier series.

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  • Understanding of Fourier series and their properties
  • Knowledge of odd and even functions in mathematics
  • Familiarity with MATLAB or Mathematica for graphical representation
  • Basic calculus, particularly integration techniques
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  • Study the properties of Fourier series, focusing on sine and cosine terms
  • Learn how to calculate the period of a function represented by a Fourier series
  • Explore how to create and interpret "deleted diagrams" in the context of Fourier analysis
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pat666
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Homework Statement


Hey,
This is a question from a sample exam we are given for our engineering maths exam. Firstly given that the Fourier series contains only "sin(x)" doesn't this mean that it is an "odd" function? Can the period be calculated from the given function easily?

Secondly is it possible to draw the "deleted diagram" from the given Fourier series (we haven't learn't this but it should be shouldn't it)? If it is can someone please draw it and then help me do question iii.

Thankyou

PS, if anyone is willing to draw it or get matlab/mathematica to, can you post it and then I will attempt the question and repost.

Homework Equations





The Attempt at a Solution

 

Attachments

  • sample exam.png
    sample exam.png
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pat666 said:

Homework Statement


Hey,
This is a question from a sample exam we are given for our engineering maths exam. Firstly given that the Fourier series contains only "sin(x)" doesn't this mean that it is an "odd" function? Can the period be calculated from the given function easily?

Secondly is it possible to draw the "deleted diagram" from the given Fourier series (we haven't learn't this but it should be shouldn't it)? If it is can someone please draw it and then help me do question iii.

Thankyou

PS, if anyone is willing to draw it or get matlab/mathematica to, can you post it and then I will attempt the question and repost.

Homework Equations


The Attempt at a Solution

If your Fourier expansion has only sine terms, it is indeed an odd function, so the An coefficient is 0. I suppose by "max and min of 1 and -1" they mean t\in[-1,1]

r(t) could be the unit step function scaled to -4, when 0<t<1. That would give you the Bn coefficient you've got, but it could've been something else too I think.

Edit: Noticed there's no -4 as a 0th term in the series, so I'm probably wrong. Looks like you need a function that integrated from -1 to 1 gives you zero, but integrated while multiplied by sin(n*t)/pi gives you -4/pi*n
 
is this a reverse square wave?
the series looks similar to this?
 

Attachments

  • Screen shot 2011-05-30 at 11.26.50 PM.png
    Screen shot 2011-05-30 at 11.26.50 PM.png
    7.8 KB · Views: 565
I'm not sure, I was hoping PF could help me out.
 

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