Structure in Galaxy Distribution. III. Fourier Transforming the Universe

We demonstrate the effectiveness of straightforward but never heretofore used 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 sophisticated methods. However we concentrate on the rarely 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. Supported by modern large scale inference methodology, this approach casts a wider net than one-parameter methods based on $F_{NL}$ for example.