My Math Forum Smooth strictly positive sine function
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 June 10th, 2014, 07:10 AM #11 Newbie   Joined: Apr 2014 From: Singapore Posts: 7 Thanks: 0 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
 June 10th, 2014, 08:45 AM #12 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,508 Thanks: 2513 Math Focus: Mainly analysis and algebra 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.
 June 11th, 2014, 05:43 AM #13 Newbie   Joined: Apr 2014 From: Singapore Posts: 7 Thanks: 0 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
June 11th, 2014, 05:59 AM   #14
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Quote:
 Originally Posted by quarkz 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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