Recently I read a paper where Fourier transformation is done from continuous k-space to discrete lattice space. The range is taken as ($-\pi$ to $\pi$). Can you explain how it can be done or any reference to that.
Discretizing a Fourier integral on a regular mesh (at the points of a Bavais lattice in arbitrary dimension), the resulting function will become periodic with the periodicity that depends on the distance between the mesh points (these facts can be explicitly verified). Depending on the function under consideration, this approximation can accurately represent that exact function (that is the function calculated without discretizing the Fourier integral) over an interval (or domain) that is embedded in the domain of periodicity of the approximate function. For details, you may wish to consult Chapter 12 of the book Numerical Recipes (Cambridge University Press), by William H. Press et al.
I think I found a softcopy of the book in the net
http://e-maxx.ru/bookz/files/numerical_recipes.pdf
Is not it?
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