Rajout de la pyramide de rejection.

Arthur HUGEAT
1 parent c9c460c6b3
Showing 2 changed files with 20 additions and 7 deletions Side-by-side Diff
ifcs2018_journal.tex
images/rejection_pyramid.pdf
-% fusionner max rejection a surface donnee v.s minimiser surface a rejection donnee 
-% demontrer comment la quantification rejette du bruit vers les hautes frequences => 6 dB de 
+% fusionner max rejection a surface donnee v.s minimiser surface a rejection donnee
+% demontrer comment la quantification rejette du bruit vers les hautes frequences => 6 dB de
 %    rejection par bit et perte si moins de bits que rejection/6
 % developper programme lineaire en incluant le decalage de bits
-% insister que avant on etait synthetisable mais pas implementable, alors que maintenant on 
-% implemente et on demontre que ca tourne 
+% insister que avant on etait synthetisable mais pas implementable, alors que maintenant on
+% implemente et on demontre que ca tourne
 %   gwen : pourquoi le FIR est desormais implementable et ne l'etait pas meme sur zedboard->new FIR ?
 % Gwen : peut-on faire un vrai banc de bruit de phase avec ce FIR, ie ajouter ADC, NCO et mixer
 %        (zedboard ou redpit)
@@ -169,7 +169,6 @@
 thanks at generator of Pseudo-Random Number (PRN) or thanks at an Analog to Digital
 Converter (ADC). Once we have a digital signal, we filter it to decrease the noise level.
 Finally we stored some burst of filtered samples before post-processing it.
-% TODO: faire un schéma
 In this particular case, we want optimize the filtering step to have the best noise
 rejection for constrain number of resource or to have the minimal resources
 consumption for a given rejection objective.
@@ -250,8 +249,6 @@
     \draw[dashed] (12,8) -- (16,8) ;
  
   \end{tikzpicture}
-
-%  \includegraphics[width=.5\linewidth]{images/fir_magnitude}
 \caption{Shape of the filter transmitted power $P$ as a function of frequency $f$:
 the passband is considered to occupy the initial 40\% of the Nyquist frequency range,
 the stopband the last 40\%, allowing 20\% transition width.}
@@ -274,6 +271,22 @@
 \includegraphics[width=\linewidth]{images/colored_custom_criterion}
 \caption{Custom criterion comparison between monolithic filter and cascade filters}
 \label{fig:custom_criterion}
+\end{figure}
+
+Thanks to this criterion we are able to automatically generate lot of fir coefficients
+and estimate their rejection. The figure~\ref{fig:rejection_pyramid} exhibits the
+rejection in function of the number of coefficients and their number of bits.
+We can observe it looks like a pyramid so the edge represents the best
+coefficient set. Indeed if we choose a number of coefficients, increasing the number
+of bits over the edge will not improve the rejection. Conversely when we choose
+a number of bits, too much increase the number of coefficients will not improve
+the rejection. Hence the best coefficient set are on the edge of pyramid.
+
+\begin{figure}
+\centering
+\includegraphics[width=\linewidth]{images/rejection_pyramid}
+\caption{Rejection as a function of number of coefficients and number of bits}
+\label{fig:rejection_pyramid}
 \end{figure}
  
 Although we have a efficient criterion to estimate the rejection of one set of coefficient
1		-% fusionner max rejection a surface donnee v.s minimiser surface a rejection donnee
2		-% demontrer comment la quantification rejette du bruit vers les hautes frequences => 6 dB de
	1	+% fusionner max rejection a surface donnee v.s minimiser surface a rejection donnee
	2	+% demontrer comment la quantification rejette du bruit vers les hautes frequences => 6 dB de
3	3	% rejection par bit et perte si moins de bits que rejection/6
4	4	% developper programme lineaire en incluant le decalage de bits
5		-% insister que avant on etait synthetisable mais pas implementable, alors que maintenant on
6		-% implemente et on demontre que ca tourne
	5	+% insister que avant on etait synthetisable mais pas implementable, alors que maintenant on
	6	+% implemente et on demontre que ca tourne
7	7	% gwen : pourquoi le FIR est desormais implementable et ne l'etait pas meme sur zedboard->new FIR ?
8	8	% Gwen : peut-on faire un vrai banc de bruit de phase avec ce FIR, ie ajouter ADC, NCO et mixer
9	9	% (zedboard ou redpit)
...	...	@@ -169,7 +169,6 @@
169	169	thanks at generator of Pseudo-Random Number (PRN) or thanks at an Analog to Digital
170	170	Converter (ADC). Once we have a digital signal, we filter it to decrease the noise level.
171	171	Finally we stored some burst of filtered samples before post-processing it.
172		-% TODO: faire un schéma
173	172	In this particular case, we want optimize the filtering step to have the best noise
174	173	rejection for constrain number of resource or to have the minimal resources
175	174	consumption for a given rejection objective.
...	...	@@ -250,8 +249,6 @@
250	249	\draw[dashed] (12,8) -- (16,8) ;
251	250
252	251	\end{tikzpicture}
253		-
254		-% \includegraphics[width=.5\linewidth]{images/fir_magnitude}
255	252	\caption{Shape of the filter transmitted power $P$ as a function of frequency $f$:
256	253	the passband is considered to occupy the initial 40\% of the Nyquist frequency range,
257	254	the stopband the last 40\%, allowing 20\% transition width.}
...	...	@@ -274,6 +271,22 @@
274	271	\includegraphics[width=\linewidth]{images/colored_custom_criterion}
275	272	\caption{Custom criterion comparison between monolithic filter and cascade filters}
276	273	\label{fig:custom_criterion}
	274	+\end{figure}
	275	+
	276	+Thanks to this criterion we are able to automatically generate lot of fir coefficients
	277	+and estimate their rejection. The figure~\ref{fig:rejection_pyramid} exhibits the
	278	+rejection in function of the number of coefficients and their number of bits.
	279	+We can observe it looks like a pyramid so the edge represents the best
	280	+coefficient set. Indeed if we choose a number of coefficients, increasing the number
	281	+of bits over the edge will not improve the rejection. Conversely when we choose
	282	+a number of bits, too much increase the number of coefficients will not improve
	283	+the rejection. Hence the best coefficient set are on the edge of pyramid.
	284	+
	285	+\begin{figure}
	286	+\centering
	287	+\includegraphics[width=\linewidth]{images/rejection_pyramid}
	288	+\caption{Rejection as a function of number of coefficients and number of bits}
	289	+\label{fig:rejection_pyramid}
277	290	\end{figure}
278	291
279	292	Although we have a efficient criterion to estimate the rejection of one set of coefficient