The data made available through this page has been updated. The most recent version of this data may be accessed through archeops_wf.cfm

Product Name
Window Functions
Mission
ARCHEOPS

Description

These two files contain the window functions (in ASCII and FITS versions) for the Archeops power spectrum bins. The integral of the window functions are normalized to 1 for each of the 16 bins and are computed between l=0 and l=768. The table contains a float array with dimension 16 x 769 (16 columns by 769 rows). The window functions are defined as follows (with implicit sum over repeated indices):

\begin{displaymath}\mathcal{C}_b=W_\ell^b \left[ \frac{\ell(\ell+1)}{2\pi}C_\ell \right]\end{displaymath}
(1)

In the MASTER framework (Hivon et al., 2002), if we define $\mathcal{M}$ as

\begin{displaymath}\mathcal{M}_{\ell^\prime \ell^{\prime\prime}}=M_{\ell^\prime......\prime\prime}}F_{\ell^{\prime\prime}}B_{\ell^{\prime\prime}}^2\end{displaymath}
(2)

Then the window function reads:

\begin{displaymath}W_\ell^b=\frac{2\pi}{\ell(\ell+1)}\left(P^b_{\ell^\prime}\ma......rime\prime\prime}}\mathcal{M}_{\ell^{\prime\prime\prime} \ell}\end{displaymath}
(3)

Where $P$ and $Q$ are the binning and reciprocal operators.

Using this definition, we have for each bin $b$:

\begin{displaymath}\sum_\ell W_\ell^b=1\end{displaymath}
(4)

Jean-Christophe Hamilton & Simon Prunet - Nov 05, 2002

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