Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Measuring the galaxy power spectrum and scale-scale correlations with
  multiresolution-decomposed covariance -- I. method   We present a method of measuring galaxy power spectrum based on the
multiresolution analysis of the discrete wavelet transformation (DWT). Since
the DWT representation has strong capability of suppressing the off-diagonal
components of the covariance for selfsimilar clustering, the DWT covariance for
popular models of the cold dark matter cosmogony generally is diagonal, or
$j$(scale)-diagonal in the scale range, in which the second scale-scale
correlations are weak. In this range, the DWT covariance gives a lossless
estimation of the power spectrum, which is equal to the corresponding Fourier
power spectrum banded with a logarithmical scaling. In the scale range, in
which the scale-scale correlation is significant, the accuracy of a power
spectrum detection depends on the scale-scale or band-band correlations. This
is, for a precision measurements of the power spectrum, a measurement of the
scale-scale or band-band correlations is needed. We show that the DWT
covariance can be employed to measuring both the band-power spectrum and second
order scale-scale correlation. We also present the DWT algorithm of the binning
and Poisson sampling with real observational data. We show that the alias
effect appeared in usual binning schemes can exactly be eliminated by the DWT
binning. Since Poisson process possesses diagonal covariance in the DWT
representation, the Poisson sampling and selection effects on the power
spectrum and second order scale-scale correlation detection are suppressed into
minimum. Moreover, the effect of the non-Gaussian features of the Poisson
sampling can be calculated in this frame.

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The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
2
The categories of this paper are: math
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The categories of this paper are: q-bio
7
The categories of this paper are: hep-th