Re: Effective epsilon used for each polarization

On Sat, 14 Oct 2006, Minghui Han wrote:
> Thanks. I now figured out what the bug is. It is due to some subtle
> difference in the storage of Fourier components between MPB and Matlab.
> In MPB, the sequence is from -N/2+1 to N/2 (assume N is an even number). But
> in Matlab, the original sequence is from 0 to N-1. After using the command
> "fftshift", the sequence is then from -N/2 to N/2-1. So in order to
> correctly reproducing curl operation in Matlab,  a one-step circular shift
> is needed.

I thought this might be the problem, which is why I mentioned that you 
should have equal numbers of +G and -G Fourier components.  Note that it's 
not a difference in the "storage" of the Fourier components, merely a 
difference in the interpretation (you don't actually need to rearrange the 
data).  The ambiguity in the interpretation is called "aliasing", and the 
-N/2 to N/2-1 choice of aliases is the optimal and standard one when doing 
Fourier differentiation.  (This is related to choosing the aliasing that 
gives a trigonometric interpolation polynomial of minimal mean-square 
slope, and which interpolates real data to real data.)

Regards,
Steven G. Johnson