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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{-0.35cm} 43 43 \vspace{-0.35cm}
% 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}{%
A. \textsc{Hugeat}$^{*}$, J. \textsc{Bernard}\\ 50 50 A. \textsc{Hugeat}$^{*}$, J. \textsc{Bernard}\\
~\\ 51 51 ~\\
FEMTO-ST, DISC dept., Besan\c con, France 52 52 FEMTO-ST, DISC dept., Besan\c con, France
} 53 53 }
\addalignedblock{0.28\textwidth}{center}{% 54 54 \addalignedblock{0.28\textwidth}{center}{%
G. \textsc{Goavec-Merou},\\ 55 55 G. \textsc{Goavec-Merou},\\
P.-Y. \textsc{Bourgeois}, J.-M \textsc{Friedt}\\ 56 56 P.-Y. \textsc{Bourgeois}, J.-M \textsc{Friedt}\\
$^{*}$FEMTO-ST, Time \& Frequency dept., Besan\c con, France 57 57 $^{*}$FEMTO-ST, Time \& Frequency 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{-.61cm} 65 65 \vspace{-.61cm}
\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{minipage}[t]{\linewidth} 69 69 %\begin{minipage}[t]{\linewidth}
%\begin{minipage}{.7\linewidth} 70 70 %\begin{minipage}{.7\linewidth}
\begin{itemize}[leftmargin=*] 71 71 \begin{itemize}[leftmargin=*]
\setlength{\itemsep}{0pt}% 72 72 \setlength{\itemsep}{0pt}%
\setlength{\parskip}{0pt}% 73 73 \setlength{\parskip}{0pt}%
\item 74 74 \item
{\bf Digital phase noise characterization}: flexibility (software defined local 75 75 {\bf Digital phase noise characterization}: flexibility (software defined local
oscillator),\\ stability (no long term drift), reconfigurabilty 76 76 oscillator),\\ stability (no long term drift), reconfigurabilty
$\Rightarrow$ {\bf software defined radio} oscillator \\ 77 77 $\Rightarrow$ {\bf software defined radio} oscillator \\
phase noise characterization 78 78 phase noise characterization
\item analog to digital conversion of radiofrequency signal, software 79 79 \item analog to digital conversion of radiofrequency signal, software
defined local oscillator, 80 80 defined local oscillator,
mixer and {\bf low pass filter} 81 81 mixer and {\bf low pass filter}
\item low pass filter uses most resources and introduces latency (phase delay 82 82 \item low pass filter uses most resources and introduces latency (phase delay
in feedback loop): needs to be optimized 83 83 in feedback loop): needs to be optimized
\end{itemize} 84 84 \end{itemize}
%\end{minipage} 85 85 %\end{minipage}
%\begin{minipage}{.28\linewidth} 86 86 %\begin{minipage}{.28\linewidth}
87 87
\vspace{-3cm}\hfill\includegraphics[width=.28\linewidth]{schema} 88 88 \vspace{-3cm}\hfill\includegraphics[width=.28\linewidth]{schema}
%\end{minipage} 89 89 %\end{minipage}
%\end{minipage} 90 90 %\end{minipage}
91 91
\vspace{1.21cm} 92 92 \vspace{1.29cm}
\hrule{\hfill} 93 93 \hrule{\hfill}
% Second part 94 94 % Second part
\vspace{-.61cm} 95 95 \vspace{-.61cm}
\newsection{Filter design and implementation strategy:} 96 96 \newsection{Filter design and implementation strategy:}
%\begin{itemize}[leftmargin=*] 97 97 %\begin{itemize}[leftmargin=*]
%\setlength{\itemsep}{0pt}% 98 98 %\setlength{\itemsep}{0pt}%
%\setlength{\parskip}{0pt}% 99 99 %\setlength{\parskip}{0pt}%
\vspace{-.40cm} 100 100 \vspace{-.40cm}
\addblock{0.44\textwidth}{ 101 101 \addblock{0.44\textwidth}{
% \begin{enumerate}[noitemsep,nolistsep] 102 102 % \begin{enumerate}[noitemsep,nolistsep]
% \item 103 103 % \item
\textbf{Classical way:}\\ 104 104 \textbf{1. Classical way:}\\
Compute the transfer function of a monolithic filter 105 105 Compute the transfer function of a monolithic filter
\begin{itemize}[label=$\Rightarrow$, noitemsep, nolistsep] 106 106 \begin{itemize}[label=$\Rightarrow$, noitemsep, nolistsep]
{\color{Green}\item Simplest way to design filter} 107 107 {\color{Green}\item Simplest way to design filter}
{\color{Green}\item Great rejection} 108 108 {\color{Green}\item Great rejection}
{\color{Red}\item Consume lot of resources on FPGA} 109 109 {\color{Red}\item Consume lot of resources on FPGA}
\end{itemize} 110 110 \end{itemize}
% \end{enumerate} 111 111 % \end{enumerate}
} 112 112 }
\addblock{0.40\textwidth}{ 113 113 \addblock{0.40\textwidth}{
% \begin{enumerate} 114 114 % \begin{enumerate}
% \setcounter{enumi}{1} 115 115 % \setcounter{enumi}{1}
% \item 116 116 % \item
\textbf{Alternative way (our focus):}\\ 117 117 \textbf{2. Alternative way (our focus):}\\
Chain of small filters 118 118 Chain of small filters
\begin{itemize}[label=$\Rightarrow$, noitemsep, nolistsep] 119 119 \begin{itemize}[label=$\Rightarrow$, noitemsep, nolistsep]
{\color{Green}\item Great rejection} 120 120 {\color{Green}\item Great rejection}
{\color{Green}\item Consume less resources on FPGA} 121 121 {\color{Green}\item Consume less resources on FPGA}
{\color{Red}\item Harder way to design filter} 122 122 {\color{Red}\item Harder way to design filter}
\end{itemize} 123 123 \end{itemize}
% \end{enumerate} 124 124 % \end{enumerate}
} 125 125 }
126 126
\vspace{-2.6cm}\hfill\includegraphics[width=.2\linewidth]{schema2} 127 127 \vspace{-2.6cm}\hfill\includegraphics[width=.2\linewidth]{schema2}
\vspace{-0.3cm} 128 128 \vspace{-0.3cm}
129 129
The 2\textsuperscript{nd} way could be considered as an optimization problem: 130 130 The 2\textsuperscript{nd} way could be considered as an optimization problem:
\begin{itemize}[noitemsep,nolistsep] 131 131 \begin{itemize}[noitemsep,nolistsep]
\item One or many {\bf performance criteria} (rejection, noise, 132 132 \item One or many {\bf performance criteria} (rejection, noise,
throughput...) 133 133 throughput...)
\item Limited {\bf resources} (on FPGA) 134 134 \item Limited {\bf resources} (area on FPGA) \hfill {\bf each FIR outputs} $y_n=\sum_{k=0}^{N_i}
135 \underbrace{b_{i_k}}_{c_i\mbox{ \footnotesize bits}}\times x_{n-k}$
\end{itemize} 135 136 \end{itemize}
Translation into a Mixed-Integer Linear Programming (MILP) with GLPK solver 136
3 degrees of freedom: 137
138 137
138 \vspace{-0.40cm}
139 \noindent Expressed as a {\bf Mixed-Integer Linear Programming} (MILP) with GLPK solver
140
141 \noindent 3 degrees of freedom: number of filters, $N_i$ number of coeff. for each filter $i$, $c_i$
142 number of bits for coefficients of filter $i$
\vspace{.1cm} 139 143 \vspace{.1cm}
%\parbox{.60\linewidth}{ 140 144 %\parbox{.60\linewidth}{
% \begin{enumerate}[noitemsep,nolistsep] 141 145 % \begin{enumerate}[noitemsep,nolistsep]
% \item 142 146 % \item
\noindent 143 147 \noindent
size of chain filters, 144
% \item 145 148 % \item
number of coefficients for each filter $i$: $N_i$, 146
% \item 147 149 % \item
number of bits for each coefficients and for each filter $i$: $c_i$ 148
% \end{enumerate} 149 150 % \end{enumerate}
%} 150 151 %}
%\end{itemize} 151 152 %\end{itemize}
\vspace{-0.5cm} 152 153 \vspace{-0.5cm}
\newsection{Filter selection} 153 154 \newsection{Filter selection}
\vspace{-0.3cm} 154 155 \vspace{-0.3cm}
\begin{itemize}[noitemsep,nolistsep] 155 156 \begin{itemize}[noitemsep,nolistsep]
\item For select the filter design we need to evaluate the rejection like: 156 157 \item For select the filter design we need to evaluate the rejection like:
157 158
% \begin{enumerate}[noitemsep,nolistsep] 158 159 % \begin{enumerate}[noitemsep,nolistsep]
% \item The mean value of rejection 159 160 % \item The mean value of rejection
% \item The median value of rejection 160 161 % \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) 161 162 % \item A custom criterion (we penalize the rejection in base band and we keep only the maximum rejection on the filter tail)
% \end{enumerate} 162 163 % \end{enumerate}
\begin{minipage}[t]{0.30\textwidth} 163 164 \begin{minipage}[t]{0.30\textwidth}
\includegraphics[width=0.95\textwidth]{images/noise-rejection-mean} 164 165 \includegraphics[width=0.95\textwidth]{images/noise-rejection-mean}
%\captionof{figure} 165 166 %\captionof{figure}
{Criterion=mean value of rejection} 166 167 {Criterion=mean value of rejection}
\end{minipage} 167 168 \end{minipage}
\begin{minipage}[t]{0.30\textwidth} 168 169 \begin{minipage}[t]{0.30\textwidth}
\includegraphics[width=0.95\textwidth]{images/noise-rejection-median} 169 170 \includegraphics[width=0.95\textwidth]{images/noise-rejection-median}
% \captionof{figure}{ 170 171 % \captionof{figure}{
{Criterion=median value of rejection} 171 172 {Criterion=median value of rejection}
\end{minipage} 172 173 \end{minipage}
\begin{minipage}[t]{0.30\textwidth} 173 174 \begin{minipage}[t]{0.30\textwidth}
\includegraphics[width=0.95\textwidth]{images/noise-rejection-custom} 174 175 \includegraphics[width=0.95\textwidth]{images/noise-rejection-custom}
% \captionof{figure} 175 176 % \captionof{figure}
{Criterion=max value of rejection} 176 177 {Criterion=max value of rejection}
\end{minipage} 177 178 \end{minipage}
\vspace{0.4cm} 178 179 \vspace{0.4cm}
\item All rejection criteria produce the same kind of result: the best filters seem to be in the edge of pyramid 179 180 \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\\ 180 181 \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} 181 182 \begin{minipage}[t]{0.30\textwidth}
\includegraphics[width=0.95\textwidth]{images/fir-mono-vs-fir-series-noise-fixe-mean.pdf} 182 183 \includegraphics[width=0.95\textwidth]{images/fir-mono-vs-fir-series-noise-fixe-mean.pdf}
% \captionof{figure}{ 183 184 % \captionof{figure}{
{Criterion=mean value of rejection} 184 185 {Criterion=mean value of rejection}
\end{minipage} 185 186 \end{minipage}
\begin{minipage}[t]{0.30\textwidth} 186 187 \begin{minipage}[t]{0.30\textwidth}
\includegraphics[width=0.95\textwidth]{images/fir-mono-vs-fir-series-noise-fixe-median.pdf} 187 188 \includegraphics[width=0.95\textwidth]{images/fir-mono-vs-fir-series-noise-fixe-median.pdf}
% \captionof{figure} 188 189 % \captionof{figure}
{Criterion=median value of rejection} 189 190 {Criterion=median value of rejection}
\end{minipage} 190 191 \end{minipage}
\begin{minipage}[t]{0.30\textwidth} 191 192 \begin{minipage}[t]{0.30\textwidth}
\includegraphics[width=0.95\textwidth]{images/fir-mono-vs-fir-series-noise-fixe-jmf.pdf} 192 193 \includegraphics[width=0.95\textwidth]{images/fir-mono-vs-fir-series-noise-fixe-jmf.pdf}
% \captionof{figure} 193 194 % \captionof{figure}
{Criterion=max value of rejection} 194 195 {Criterion=max value of rejection}
\end{minipage} 195 196 \end{minipage}
\vspace{0.4cm} 196 197 \vspace{0.4cm}
\item {\bf Rejection}: the last configuration is better than the first but worse 197 198 \item {\bf Rejection}: the last configuration is better than the first but worse
than the monolithic filter 198 199 than the monolithic filter
\item Resources {\bf consumption}: last filter is better than the single monolithic filter 199 200 \item Resource {\bf consumption} assessed by {\bf synthesizing designs in Vivado} (2017): filter cascade uses less
(monolithic does not fit in available resources) 200 201 resources than a single monolithic filter (too large to fit in Zedboard's Zynq 7020)
\vspace{-.33cm} 201 202 \vspace{-.33cm}
\begin{center} 202 203 \begin{center}
\begin{tabular}{|c|ccccc|}\hline 203 204 \begin{tabular}{|c|ccccc|}\hline
FIR & BlockRAM36 & BlockRAM18 & LookUpTables & DSP & rejection (dB)\\\hline\hline 204 205 FIR & BlockRAM36 & BlockRAM18 & LookUpTables & DSP & rejection (dB)\\\hline\hline
1 (monolithic) & 1 & 0 & {\color{Red}76183} & 220 & -162 \\ 205 206 1 (monolithic) & 1 & 0 & {\color{Red}76183} & 220 & -162 \\
5 & 0 & 5 & {\color{Green}18597} & 220 & -160 \\ 206 207 5 & 0 & 5 & {\color{Green}18597} & 220 & -160 \\
10 & 0 & 8 & {\color{Green}24729} & 220 & -161 \\\hline\hline 207 208 10 & 0 & 8 & {\color{Green}24729} & 220 & -161 \\\hline\hline
\textbf{Zynq 7020} & \textbf{140} & \textbf{280} & \textbf{53200} & \textbf{220} & \\\hline 208 209 \textbf{Zynq 7020} & \textbf{140} & \textbf{280} & \textbf{53200} & \textbf{220} & \\\hline
\end{tabular} 209 210 \end{tabular}
% \captionof{table}{Resources consumption when we use the configuration with the custom criterion} 210 211 % \captionof{table}{Resources consumption when we use the configuration with the custom criterion}
\end{center} 211 212 \end{center}
\item Series of filters: targetd rejection level (-160~dB) reached since less 212 213 \item Filter cascade: {\bf targeted rejection level} (-160~dB) reached with the max(rejection) criterion
resources are needed than with a monolithic filter 213
\end{itemize} 214 214 \end{itemize}
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