Structure in Galaxy Distribution. III. Fourier Transforming the Universe
  We demonstrate the effectiveness of a relatively straightforward analysis of
the complex 3D Fourier transform of galaxy coordinates derived from redshift
surveys. Numerical demonstrations of this approach are carried out on a
volume-limited sample of the Sloan Digital Sky Survey redshift survey. The
direct unbinned transform yields a complex 3D data cube quite similar to that
from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In
both cases deconvolution of the sampling window function yields estimates of
the true transform. Simple power spectrum estimates from these transforms are
roughly consistent with those using more elaborate methods. However we
concentrate on the less often studied Fourier phase spectrum, a simple and
general framework for characterizing non-Gaussianity, more easily interpretable
than the tangled, incomplete multi-point methods conventionally used. No
significant signature of non-Gaussianity has been found in the relatively small
data set analyzed, but we identify some threads of modern large scale inference
methodology that will presumably yield detections in new wider and deeper
surveys.
