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June 10th, 2014, 07:10 AM   #11
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Btw, I realised that while the values are close, the gradients are rather different. Is there any way to make the gradients similar too?

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June 10th, 2014, 08:45 AM   #12
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The limit as $n \to \infty$ of the Fourier Series is the original function $|sin{x}|$. So at the limit the gradients and the values are the same.

In other words, you should take more terms. Of course, the closer you get to $x = n\pi$ the greater the dfference in the gradient, because $|sin{x}|$ is not smooth at $x = n\pi$ while the Fourier Series is smooth everywhere.
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June 11th, 2014, 05:43 AM   #13
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Btw, I realised that while the values are close, the gradients are rather different. Is there any way to make the gradients similar too?

Thanks
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June 11th, 2014, 05:59 AM   #14
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Quote:
Originally Posted by quarkz View Post
Hmm ... (sinx)^2 / x is an interesting graph... too bad it's skew to one side.
The skew is caused by the denominator. Using just $\displaystyle \sin^2x$ will create a periodic, positive function that always has the same maximum magnitude at each peak.
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