Decomposition of spectra from redshift distortion maps

We develop an optimized technique to extract density–density and velocity–velocity spectra out of observed spectra in redshift space. The measured spectra of the distribution of haloes from redshift distorted mock map are binned into two-dimensional coordinates in Fourier space so as to be decomposed into both spectra using angular projection dependence. With the threshold limit introduced to minimize non-linear suppression, the decomposed velocity–velocity spectra are reasonably well measured up to scale k= 0.07 h Mpc−1, and the measured variances using our method are consistent with errors predicted from a Fisher matrix analysis. The detectability is extendable to k∼ 0.1 h Mpc−1 with more conservative bounds at the cost of weakened constraint.