The DWT power spectrum analysis of the large scale structure in the universe : Method and simulation tests

Based on the discrete wavelet transformation ( DWT), we present a pixelized method of estimating the power spectra of galaxy samples. With local properties of wavelet both in physical and wavenumber spaces, DWT power spectrum is equal to the corresponding band average of Fourier power spectrum. The DWT estimator is optimized in the sense that the spatial resolution is adaptive automatically to the perturbation wavelength to be studied. Under the assumption of ergodicity, the spatial average of local DWT fluctuation modes provides a fair estimation of the ensemble average. We test DWT spectra of four typical cold dark matter (CDM) structure formation models with numerical simulations. To consider the infections of various observation effects to the DWT spectra, we introduce irregular survey geometries, a given sampling rate, radial selection effects and redshift distortion effects into our mock samples. The numerical results show that, owing to its local properties, DWT spectrum is less affected by the sampling rate, survey geometry, and statistical ensemble fluctuations. With fast wavelet decomposition algorithm, DWT can be used to analyze large survey samples, which is of direct significance in precise measurement of the cosmological parameters from the galaxy redshift surveys of next generation.