jfriedt / IFCS2018 article

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ajouts suite a discussion avec Arthur

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... ... @@ -89,7 +89,7 @@
89 89 %\end{minipage}
90 90 %\end{minipage}
91 91  
92   -\vspace{1.21cm}
  92 +\vspace{1.29cm}
93 93 \hrule{\hfill}
94 94 % Second part
95 95 \vspace{-.61cm}
... ... @@ -101,7 +101,7 @@
101 101 \addblock{0.44\textwidth}{
102 102 % \begin{enumerate}[noitemsep,nolistsep]
103 103 % \item
104   -\textbf{Classical way:}\
  104 +\textbf{1. Classical way:}\
105 105 Compute the transfer function of a monolithic filter
106 106 \begin{itemize}[label=$\Rightarrow$, noitemsep, nolistsep]
107 107 {\color{Green}\item Simplest way to design filter}
... ... @@ -114,7 +114,7 @@
114 114 % \begin{enumerate}
115 115 % \setcounter{enumi}{1}
116 116 % \item
117   -\textbf{Alternative way (our focus):}\
  117 +\textbf{2. Alternative way (our focus):}\
118 118 Chain of small filters
119 119 \begin{itemize}[label=$\Rightarrow$, noitemsep, nolistsep]
120 120 {\color{Green}\item Great rejection}
121 121  
122 122  
123 123  
124 124  
125 125  
... ... @@ -131,21 +131,22 @@
131 131 \begin{itemize}[noitemsep,nolistsep]
132 132 \item One or many {\bf performance criteria} (rejection, noise,
133 133 throughput...)
134   - \item Limited {\bf resources} (on FPGA)
  134 + \item Limited {\bf resources} (area on FPGA) \hfill {\bf each FIR outputs} $y_n=\sum_{k=0}^{N_i}
  135 +\underbrace{b_{i_k}}_{c_i\mbox{ \footnotesize bits}}\times x_{n-k}$
135 136 \end{itemize}
136   - Translation into a Mixed-Integer Linear Programming (MILP) with GLPK solver
137   - 3 degrees of freedom:
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 $i$
139 143 \vspace{.1cm}
140 144 %\parbox{.60\linewidth}{
141 145 % \begin{enumerate}[noitemsep,nolistsep]
142 146 % \item
143 147 \noindent
144   -size of chain filters,
145 148 % \item
146   -number of coefficients for each filter $i$: $N_i$,
147 149 % \item
148   -number of bits for each coefficients and for each filter $i$: $c_i$
149 150 % \end{enumerate}
150 151 %}
151 152 %\end{itemize}
... ... @@ -196,8 +197,8 @@
196 197 \vspace{0.4cm}
197 198 \item {\bf Rejection}: the last configuration is better than the first but worse
198 199 than the monolithic filter
199   - \item Resources {\bf consumption}: last filter is better than the single monolithic filter
200   -(monolithic does not fit in available resources)
  200 + \item Resource {\bf consumption} assessed by {\bf synthesizing designs in Vivado} (2017): filter cascade uses less
  201 +resources than a single monolithic filter (too large to fit in Zedboard's Zynq 7020)
201 202 \vspace{-.33cm}
202 203 \begin{center}
203 204 \begin{tabular}{|c|ccccc|}\hline
... ... @@ -209,8 +210,7 @@
209 210 \end{tabular}
210 211 % \captionof{table}{Resources consumption when we use the configuration with the custom criterion}
211 212 \end{center}
212   - \item Series of filters: targetd rejection level (-160~dB) reached since less
213   -resources are needed than with a monolithic filter
  213 + \item Filter cascade: {\bf targeted rejection level} (-160~dB) reached with the max(rejection) criterion
214 214 \end{itemize}
215 215 \hrule{\hfill}
216 216  
... ... @@ -7,6 +7,46 @@
7 7 Single
8 8 -2
9 9 1200 2
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11 51 1 3 0 1 0 7 50 -1 -1 0.000 1 0.0000 6210 4140 180 180 6210 4140 6390 4140
12 52 2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 3
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27 67 6390 4185 6525 4185
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47 78 0.000 1.000 1.000 0.000
... ... @@ -50,5 +81,5 @@
50 81 4 0 0 50 -1 0 12 0.0000 4 135 405 5985 4635 NCO\001
51 82 4 0 0 50 -1 0 8 0.0000 4 120 105 6390 4320 Q\001
52 83 4 0 0 50 -1 0 8 0.0000 4 90 45 6390 4050 I\001
53   -4 0 0 50 -1 0 12 1.5708 4 120 345 7335 4320 atan\001
  84 +4 0 4 50 -1 0 12 0.0000 4 15 135 7065 4140 ...\001
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