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I don't understand the equation37 in simulate ocean water by Jerry Tessendorf.The result is all complex number, how to be the slope.Even if I compute the magnitude of it,the result is just positive which is obvious wrong.As There must be some points whose slope is negative.Who can help me.Thank you.

http://www-evasion.imag.fr/Membres/Fabrice.Neyret/NaturalScenes/fluids/water/waves/fluids-nuages/waves/Jonathan/articlesCG/simulating-ocean-water-01.pdf

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    Do you mean that they should be small?But I found that they are not small enough compare to the real part.2012-11-28

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If $h(x)$ is a real valued function we have that since $h(x) = \bar{h}(x)$ that its Fourier series

$ h(x) \approx \sum \tilde{h}(k) \exp ikx = \sum \bar{\tilde{h}}(k) \exp -ikx \approx \bar{h}(x)$

So $\tilde{h}(k) = \bar{\tilde{h}}(-k)$. This is a fundamental property of the Fourier transform of real valued functions.

Now if we write

$ \nabla h(x) \approx \sum i k \tilde{h}(k) \exp ikx = \sum \eta(k) \exp ikx $

we note that

$ \bar\eta(k) = \eta(-k) $

by a direct computation. And hence

$ \nabla h(x) = \overline{\nabla h}(x) $

is a real valued function.

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    If$n$is a even number,then h*(k) = h(n-k).If$n$is a odd number,then h*(k) = h(n-1-k).These can guarantee that the result of the IDFT is real number.I don't quite understand what you're saying,but thx.2012-12-05