memo describing APERTIF Anti-Aliasing Filter (AAF)

applications/apertif/doc/AAF_APERTIF/ASTRON_RP_1549_Apertif_Anti_Aliasing_Filter.tex

+\documentclass[a4paper,10pt]{astron}
+
+\usepackage{graphicx,amsmath,color}
+
+% page header information
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+\renewcommand{\theAuthor}{E.~Kooistra, S.J.~Wijnholds}
+\renewcommand{\theAuthorOrganization}{ASTRON}
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+\renewcommand{\theChecked}{A.~Mika}
+\renewcommand{\theCheckedOrganization}{ASTRON}
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+\renewcommand{\theAuthorisation}{A.~Mika}
+\renewcommand{\theAuthorisationOrganization}{ASTRON}
+\renewcommand{\theAuthorisationDate}{}
+
+% title of the document
+\renewcommand{\theTitle}{APERTIF Anti-Aliasing Filter}
+
+% footer information
+\renewcommand{\theProject}{APERTIF}
+\renewcommand{\theDepartment}{R\&D}
+\renewcommand{\theFootDocNr}{ASTRON-RP-1549}
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+
+% distribution list
+\renewcommand{\dGList}{%
+E.~Kooistra\\
+A.~Mika\\
+R.~Oonk\\
+T.~Oosterloo\\
+S.~van~der~Tol\\
+M.A.W.~Verheijen\\
+S.J.~Wijnholds
+}
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+-}
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+
+\begin{document}
+
+\maketitle
+\newpage
+
+\theDistributionList
+\theDocumentRevision
+\newpage
+
+\tableofcontents
+\newpage
+
+\section{Introduction}
+
+\subsection{Purpose of this report}
+
+In the APERTIF signal chains, Nyquist-sampled polyphase filter banks are used to split the baseband signal in 781-kHz wide subbands, which are then further split into 12-kHz wide frequency channels. Due to the finite length of the finite impulse response (FIR) filters used, the frequency response of these filters is not infinitely sharp. This causes aliasing effects at the edges of the subbands that become visible after channel separation. A similar frequency separation structure is used in LOFAR. As LOFAR observations mostly concern astronomical signals with a reasonably wide frequency response, the solution adopted in LOFAR is to simply flag the channels near the edges of the subband. This approach may not work for APERTIF, since APERTIF will mostly be used to conduct spectral line observations.
+
+In this document, we
+\begin{enumerate}
+\item assess the impact of the aliasing effect at the subband edges on spectral line observations with the goal of determining the need for corrective processing steps to mitigate this effect;
+\item discuss possible solutions and their impact the APERTIF signal chain and observing strategy;
+\item select the most suitable solution and describe it in sufficient detail to provide a good starting point for implementation in the APERTIF system.
+\end{enumerate}
+
+\subsection{Outline of this document}
+
+In the next section, we present a theoretical framework to describe the FIR filter response and use it to demonstrate the effect it has on the observed spectra. This section is concluded with an assessment on the potential impact on APERTIF observations. In Sec.~\ref{sec:corrective_measures}, we give an overview of possible corrective measures and assess their impact on the APERTIF signal chain and observing strategy. Based on that assessment, a preferred solution is proposed, which is described in more detail in Sec.~\ref{sec:AAF}. This detailed description includes an assessment of the level to which aliasing effects are reduced as well as an updated overview of the APERTIF signal chain that is sufficiently detailed to start work on the implementation of the solution. The code of the key routines used for the simulations presented in this report is provided in the Appendix.
+
+\section{FIR filter response}
+\subsection{Theoretical description}
+\subsection{Impact on spectra}
+\subsection{Impact on observations}
+% source smearing? missed lindes? velocity field reconstruction issues?
+
+\section{Corrective measures}
+\label{sec:corrective_measures}
+\subsection{Flag and ignore affected channels}
+\subsection{Oversampled polyphase filter bank}
+\subsection{Anti-aliasing filter}
+\subsection{Re-observing with local oscillator tuning}
+\subsection{Preferred solution}
+
+\section{Anti-aliasing filter implementation}
+\label{sec:AAF}
+{\color{red} SJW: it is assumed that the outcome of the assessment of different options will be that the anti-aliasing filter is the preferred solution. We should, however, remain willing to accept a different solution if the assessment in the previous section dictates otherwise.}
+
+\addtocontents{toc}{\contentsline{section}{References}{\pageref{literature}}}
+\bibliographystyle{IEEEtran}
+\bibliography{refs}
+\label{literature}
+
+\appendix
+
+\section{Matlab code}
+\label{sec:app_code}
+
+\end{document}