Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Correcting for the alias effect when measuring the power spectrum using
  FFT   Because of mass assignment onto grid points in the measurement of the power
spectrum using the Fast Fourier Transform (FFT), the raw power spectrum $\la
|\delta^f(k)|^2\ra$ estimated with FFT is not the same as the true power
spectrum $P(k)$. In this paper, we derive the formula which relates $\la
|\delta^f(k)|^2\ra$ to $P(k)$. For a sample of $N$ discrete objects, the
formula reads: $\la |\delta^f(k)|^2\ra=\sum_{\vec n}
[|W(\kalias)|^2P(\kalias)+1/N|W(\kalias)|^2]$, where $W(\vec k)$ is the Fourier
transform of the mass assignment function $W(\vec r)$, $k_N$ is the Nyquist
wavenumber, and $\vec n$ is an integer vector. The formula is different from
that in some of previous works where the summation over $\vec n$ is neglected.
For the NGP, CIC and TSC assignment functions, we show that the shot noise term
$\sum_{\vec n} 1/N|W(\kalias)|^2]$ can be expressed by simple analytical
functions. To reconstruct $P(k)$ from the alias sum $\sum_{\vec
n}|W(\kalias)|^2 P(\kalias)$, we propose an iterative method. We test the
method by applying it to an N-body simulation sample, and show that the method
can successfully recover $P(k)$. The discussion is further generalized to
samples with observational selection effects.

35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex