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\documentclass[a4paper]{article} 1 1 \documentclass[a4paper]{article}
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31 31
\begin{document} 32 32 \begin{document}
33 33
% Title 34 34 % Title
\begin{center} 35 35 \begin{center}
\textbf{{\scshape 36 36 \textbf{{\scshape
\LARGE\color{OliveGreen} 37 37 \LARGE\color{OliveGreen}
Filter optimization for real time digital processing of radiofrequency signals: application 38 38 Filter optimization for real time digital processing of radiofrequency signals: application
to oscillator metrology 39 39 to oscillator metrology
\\}} 40 40 \\}}
\end{center} 41 41 \end{center}
42 42
\vspace{-0.7cm} 43 43 \vspace{-0.7cm}
% Authors 44 44 % Authors
\begin{center} 45 45 \begin{center}
\addalignedblock{0.18\textwidth}{flushleft}{% 46 46 \addalignedblock{0.18\textwidth}{flushleft}{%
\includegraphics[height=1.6cm]{images/logo_ubfc} 47 47 \includegraphics[height=1.6cm]{images/logo_ubfc}
} 48 48 }
\addalignedblock{0.28\textwidth}{center}{% 49 49 \addalignedblock{0.28\textwidth}{center}{%
G. \textsc{Goavec-M\'erou},\\ 50 50 G. \textsc{Goavec-M\'erou},\\
P.-Y. \textsc{Bourgeois}, J.-M \textsc{Friedt}\\ 51 51 P.-Y. \textsc{Bourgeois}, J.-M \textsc{Friedt}\\
$^{*}$FEMTO-ST, Time \& Frequency dept., Besan\c con, France 52 52 $^{*}$FEMTO-ST, Time \& Frequency dept., Besan\c con, France
} 53 53 }
\addalignedblock{0.28\textwidth}{center}{% 54 54 \addalignedblock{0.28\textwidth}{center}{%
A. \textsc{Hugeat}$^{*}$, J. \textsc{Bernard}\\ 55 55 A. \textsc{Hugeat}$^{*}$, J. \textsc{Bernard}\\
~\\ 56 56 ~\\
FEMTO-ST, DISC dept., Besan\c con, France 57 57 FEMTO-ST, DISC dept., Besan\c con, France
} 58 58 }
\addalignedblock{0.18\textwidth}{flushright}{% 59 59 \addalignedblock{0.18\textwidth}{flushright}{%
\includegraphics[height=1.4cm]{images/logo_femto} 60 60 \includegraphics[height=1.4cm]{images/logo_femto}
} 61 61 }
\end{center} 62 62 \end{center}
63 63
% First part 64 64 % First part
\vspace{-.71cm} 65 65 \vspace{-.71cm}
\newsection{Digital signal processing of ultrastable clock signals} 66 66 \newsection{Digital signal processing of ultrastable clock signals}
67 67
\vspace{-.21cm} 68 68 \vspace{-.21cm}
\begin{itemize}[leftmargin=*] 69 69 \begin{itemize}[leftmargin=*]
\setlength{\itemsep}{0pt}% 70 70 \setlength{\itemsep}{0pt}%
\setlength{\parskip}{0pt}% 71 71 \setlength{\parskip}{0pt}%
\item 72 72 \item
{\bf Digital phase noise characterization}: flexibility (software defined local 73 73 {\bf Digital phase noise characterization}: flexibility (software defined local
oscillator), stability (no long term drift), reconfigurabilty 74 74 oscillator), stability (no long term drift), reconfigurabilty
$\Rightarrow$ {\bf software defined radio} oscillator phase noise 75 75 $\Rightarrow$ {\bf software defined radio} oscillator phase noise
characterization 76 76 characterization
\item analog to digital conversion of radiofrequency signal, software 77 77 \item analog to digital conversion of radiofrequency signal, software
defined local oscillator, mixer and {\bf low pass filter} 78 78 defined local oscillator, mixer and {\bf low pass filter}
\item low pass filter uses most resources and introduces latency (phase delay 79 79 \item low pass filter uses most resources and introduces latency (phase delay
in feedback loop): needs to be optimized 80 80 in feedback loop): needs to be optimized
\end{itemize} 81 81 \end{itemize}
82 82
\vspace{-.21cm} 83 83 \vspace{-.21cm}
\hrule{\hfill} 84 84 \hrule{\hfill}
% Second part 85 85 % Second part
\vspace{-.71cm} 86 86 \vspace{-.71cm}
\newsection{Filter design and implementation strategy:} 87 87 \newsection{Filter design and implementation strategy:}
%\begin{itemize}[leftmargin=*] 88 88 %\begin{itemize}[leftmargin=*]
%\setlength{\itemsep}{0pt}% 89 89 %\setlength{\itemsep}{0pt}%
%\setlength{\parskip}{0pt}% 90 90 %\setlength{\parskip}{0pt}%
\vspace{-.41cm} 91 91 \vspace{-.41cm}
\addblock{0.48\textwidth}{ 92 92 \addblock{0.48\textwidth}{
\begin{enumerate}[noitemsep,nolistsep] 93 93 \begin{enumerate}[noitemsep,nolistsep]
\item \textbf{Classical way:}\\ 94 94 \item \textbf{Classical way:}\\
Compute the transfer function of a monolithic filter 95 95 Compute the transfer function of a monolithic filter
\begin{itemize}[label=$\Rightarrow$, noitemsep, nolistsep] 96 96 \begin{itemize}[label=$\Rightarrow$, noitemsep, nolistsep]
{\color{Green}\item Simplest way to design filter} 97 97 {\color{Green}\item Simplest way to design filter}
{\color{Green}\item Great rejection} 98 98 {\color{Green}\item Great rejection}
{\color{Red}\item Consume lot of resources on FPGA} 99 99 {\color{Red}\item Consume lot of resources on FPGA}
\end{itemize} 100 100 \end{itemize}
\end{enumerate} 101 101 \end{enumerate}
} 102 102 }
\addblock{0.48\textwidth}{ 103 103 \addblock{0.48\textwidth}{
\begin{enumerate} 104 104 \begin{enumerate}
\setcounter{enumi}{1} 105 105 \setcounter{enumi}{1}
\item \textbf{Alternative way (our focus):}\\ 106 106 \item \textbf{Alternative way (our focus):}\\
Chain of little filters 107 107 Chain of small filters
\begin{itemize}[label=$\Rightarrow$, noitemsep, nolistsep] 108 108 \begin{itemize}[label=$\Rightarrow$, noitemsep, nolistsep]
{\color{Green}\item Great rejection} 109 109 {\color{Green}\item Great rejection}
{\color{Green}\item Consume less resources on FPGA} 110 110 {\color{Green}\item Consume less resources on FPGA}
{\color{Red}\item Harder way to design filter} 111 111 {\color{Red}\item Harder way to design filter}
\end{itemize} 112 112 \end{itemize}
\end{enumerate} 113 113 \end{enumerate}
} 114 114 }
The 2\textsuperscript{nd} way could be considered as an optimization problem: 115 115 The 2\textsuperscript{nd} way could be considered as an optimization problem:
\begin{itemize}[noitemsep,nolistsep] 116 116 \begin{itemize}[noitemsep,nolistsep]
\item One or many {\bf performance criteria} (rejection, noise, 117 117 \item One or many {\bf performance criteria} (rejection, noise,
throughput...) 118 118 throughput...)
\item Limited {\bf resources} (on FPGA) 119 119 \item Limited {\bf resources} (on FPGA)
\end{itemize} 120 120 \end{itemize}
Translation into a Mixed-Integer Linear Programming (MILP) with GLPK solver 121 121 Translation into a Mixed-Integer Linear Programming (MILP) with GLPK solver
3 degrees of freedom: 122 122 3 degrees of freedom:
123 123
\vspace{.1cm} 124 124 \vspace{.1cm}
\hfill 125 125 \hfill
\parbox{.60\linewidth}{ 126 126 \parbox{.60\linewidth}{
\begin{enumerate}[noitemsep,nolistsep] 127 127 \begin{enumerate}[noitemsep,nolistsep]
\item The size of chain filters 128 128 \item The size of chain filters
\item The number of coefficients for each filter $i$: $N_i$ 129 129 \item The number of coefficients for each filter $i$: $N_i$
\item The number of bits for each coefficients and for each filter $i$: $c_i$ 130 130 \item The number of bits for each coefficients and for each filter $i$: $c_i$
\end{enumerate} 131 131 \end{enumerate}
} 132 132 }
%\end{itemize} 133 133 %\end{itemize}
\vspace{-1.0cm} 134 134 \vspace{-1.0cm}
\newsection{Filter selection} 135 135 \newsection{Filter selection}
\vspace{-0.3cm} 136 136 \vspace{-0.3cm}
\begin{itemize}[noitemsep,nolistsep] 137 137 \begin{itemize}[noitemsep,nolistsep]
\item For select the filter design we need to evaluate the rejection like: 138 138 \item For select the filter design we need to evaluate the rejection like:
\begin{enumerate}[noitemsep,nolistsep] 139 139 \begin{enumerate}[noitemsep,nolistsep]
\item The mean value of rejection 140 140 \item The mean value of rejection
\item The median value of rejection 141 141 \item The median value of rejection
\item A custom criterion (we penalize the rejection in base band and we keep only the maximum rejection on the filter tail) 142 142 \item A custom criterion (we penalize the rejection in base band and we keep only the maximum rejection on the filter tail)
\end{enumerate} 143 143 \end{enumerate}
\begin{minipage}[t]{0.30\textwidth} 144 144 \begin{minipage}[t]{0.30\textwidth}
\includegraphics[width=0.95\textwidth]{images/noise-rejection-mean} 145 145 \includegraphics[width=0.95\textwidth]{images/noise-rejection-mean}
\captionof{figure}{Mean criterion} 146 146 \captionof{figure}{Mean criterion}
\end{minipage} 147 147 \end{minipage}
\begin{minipage}[t]{0.30\textwidth} 148 148 \begin{minipage}[t]{0.30\textwidth}
\includegraphics[width=0.95\textwidth]{images/noise-rejection-median} 149 149 \includegraphics[width=0.95\textwidth]{images/noise-rejection-median}
\captionof{figure}{Median criterion} 150 150 \captionof{figure}{Median criterion}
\end{minipage} 151 151 \end{minipage}
\begin{minipage}[t]{0.30\textwidth} 152 152 \begin{minipage}[t]{0.30\textwidth}
\includegraphics[width=0.95\textwidth]{images/noise-rejection-custom} 153 153 \includegraphics[width=0.95\textwidth]{images/noise-rejection-custom}
\captionof{figure}{Custom criterion} 154 154 \captionof{figure}{Custom criterion}
\end{minipage} 155 155 \end{minipage}
\item All rejection criteria produce the same kind of result: the best filters seem to be in the edge of pyramid 156 156 \item All rejection criteria produce the same kind of result: the best filters seem to be in the edge of pyramid
\item For each criteria, we associate the rejection to the related filter and we let GLPK choose the best configuration\\ 157 157 \item For each criteria, we associate the rejection to the related filter and we let GLPK choose the best configuration\\
\begin{minipage}[t]{0.30\textwidth} 158 158 \begin{minipage}[t]{0.30\textwidth}
\includegraphics[width=0.95\textwidth]{images/fir-mono-vs-fir-series-noise-fixe-mean.pdf} 159 159 \includegraphics[width=0.95\textwidth]{images/fir-mono-vs-fir-series-noise-fixe-mean.pdf}
\captionof{figure}{Mean criterion} 160 160 \captionof{figure}{Mean criterion}
\end{minipage} 161 161 \end{minipage}
\begin{minipage}[t]{0.30\textwidth} 162 162 \begin{minipage}[t]{0.30\textwidth}
\includegraphics[width=0.95\textwidth]{images/fir-mono-vs-fir-series-noise-fixe-median.pdf} 163 163 \includegraphics[width=0.95\textwidth]{images/fir-mono-vs-fir-series-noise-fixe-median.pdf}
\captionof{figure}{Median criterion} 164 164 \captionof{figure}{Median criterion}
\end{minipage} 165 165 \end{minipage}
\begin{minipage}[t]{0.30\textwidth} 166 166 \begin{minipage}[t]{0.30\textwidth}
\includegraphics[width=0.95\textwidth]{images/fir-mono-vs-fir-series-noise-fixe-jmf.pdf} 167 167 \includegraphics[width=0.95\textwidth]{images/fir-mono-vs-fir-series-noise-fixe-jmf.pdf}
\captionof{figure}{Custom criterion} 168 168 \captionof{figure}{Custom criterion}
\end{minipage} 169 169 \end{minipage}
170 <<<<<<< HEAD
\item {\bf Rejection}: the last configuration is better than the first but worse 170 171 \item {\bf Rejection}: the last configuration is better than the first but worse
than the monolithic filter 171 172 than the monolithic filter
\item Resources {\bf consumption}: last filter is better than the single monolithic filter 172 173 \item Resources {\bf consumption}: last filter is better than the single monolithic filter
(monolithic does not fit in available resources) 173 174 (monolithic does not fit in available resources)
\vspace{-.33cm} 174 175 \vspace{-.33cm}
176 =======
177 \item For the rejection: the last configuration is better than the first one but it's worst than monolithic filter
178 \item For the resources consumption: the last one is better than the single filter
179 >>>>>>> de0f544773b03c4215f07cea693fc7eb145ff20a
\begin{center} 175 180 \begin{center}
\begin{tabular}{|c|ccccc|}\hline 176 181 \begin{tabular}{|c|ccccc|}\hline
FIR & BlockRAM36 & BlockRAM18 & LookUpTables & DSP & rejection (dB)\\\hline\hline 177 182 FIR & BlockRAM36 & BlockRAM18 & LookUpTables & DSP & rejection (dB)\\\hline\hline
1 (monolithic) & 1 & 0 & {\color{Red}76183} & 220 & -162 \\ 178 183 1 (monolithic) & 1 & 0 & {\color{Red}76183} & 220 & -162 \\
5 & 0 & 5 & {\color{Green}18597} & 220 & -160 \\ 179 184 5 & 0 & 5 & {\color{Green}18597} & 220 & -160 \\
10 & 0 & 8 & {\color{Green}24729} & 220 & -161 \\\hline\hline 180 185 10 & 0 & 8 & {\color{Green}24729} & 220 & -161 \\\hline\hline
\textbf{Zynq 7020} & \textbf{140} & \textbf{280} & \textbf{53200} & \textbf{220} & \\\hline 181 186 \textbf{Zynq 7020} & \textbf{140} & \textbf{280} & \textbf{53200} & \textbf{220} & \\\hline
\end{tabular} 182 187 \end{tabular}
% \captionof{table}{Resources consumption when we use the configuration with the custom criterion} 183 188 % \captionof{table}{Resources consumption when we use the configuration with the custom criterion}
\end{center} 184 189 \end{center}
\item Series of filters: targetd rejection level (-160~dB) reached since less 185 190 \item Series of filters: targetd rejection level (-160~dB) reached since less