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>Measuring the galaxy power spectrum and scale-scale correlations with multiresolution-decomposed covariance -- I. method
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Measuring the galaxy power spectrum and scale-scale correlations with multiresolution-decomposed covariance -- I. method
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机译：测量星系功率谱和尺度尺度相关性 多分辨率 - 分解协方差 - I.方法
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摘要
We present a method of measuring galaxy power spectrum based on themultiresolution analysis of the discrete wavelet transformation (DWT). Sincethe DWT representation has strong capability of suppressing the off-diagonalcomponents of the covariance for selfsimilar clustering, the DWT covariance forpopular models of the cold dark matter cosmogony generally is diagonal, or$j$(scale)-diagonal in the scale range, in which the second scale-scalecorrelations are weak. In this range, the DWT covariance gives a losslessestimation of the power spectrum, which is equal to the corresponding Fourierpower spectrum banded with a logarithmical scaling. In the scale range, inwhich the scale-scale correlation is significant, the accuracy of a powerspectrum detection depends on the scale-scale or band-band correlations. Thisis, for a precision measurements of the power spectrum, a measurement of thescale-scale or band-band correlations is needed. We show that the DWTcovariance can be employed to measuring both the band-power spectrum and secondorder scale-scale correlation. We also present the DWT algorithm of the binningand Poisson sampling with real observational data. We show that the aliaseffect appeared in usual binning schemes can exactly be eliminated by the DWTbinning. Since Poisson process possesses diagonal covariance in the DWTrepresentation, the Poisson sampling and selection effects on the powerspectrum and second order scale-scale correlation detection are suppressed intominimum. Moreover, the effect of the non-Gaussian features of the Poissonsampling can be calculated in this frame.
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