  We explore features of redshift distortion in Fourier analysis of N-body
simulations. The phases of the Fourier modes of the dark matter density
fluctuation are generally shifted by the peculiar motion along the line of
sight, the induced phase shift is stochastic and has probability distribution
function (PDF) symmetric to the peak at zero shift while the exact shape
depends on the wave vector, except on very large scales where phases are
invariant by linear perturbation theory. Analysis of the phase shifts motivates
our phenomenological models for the bispectrum in redshift space. Comparison
with simulations shows that our toy models are very successful in modeling
bispectrum of equilateral and isosceles triangles at large scales. In the
second part we compare the monopole of the power spectrum and bispectrum in the
radial and plane-parallel distortion to test the plane-parallel approximation.
We confirm the results of Scoccimarro (2000) that difference of power spectrum
is at the level of 10%, in the reduced bispectrum such difference is as small
as a few percents. However, on the plane perpendicular to the line of sight of
k_z=0, the difference in power spectrum between the radial and plane-parallel
approximation can be more than 10%, and even worse on very small scales. Such
difference is prominent for bispectrum, especially for those configurations of
tilted triangles. The non-Gaussian signals under radial distortion on small
scales are systematically biased downside than that in plane-parallel
approximation, while amplitudes of differences depend on the opening angle of
the sample to the observer. The observation gives warning to the practice of
using the power spectrum and bispectrum measured on the k_z=0 plane as
estimation of the real space statistics.
