relecture finale JMF

jfriedt
1 parent 6de4fd10e7
Showing 2 changed files with 65 additions and 42 deletions Side-by-side Diff
ifcs2018_journal.tex
ifcs2018_journal_reponse.tex
@@ -292,10 +292,11 @@
  
 In the transition band, the behavior of the filter is left free, we only {\color{red}define} the passband and the stopband characteristics.
 % r2.7
-% Our initial criterion considered the mean value of the stopband rejection, as shown in figure~\ref{fig:mean_criterion}. This criterion
-% yields unacceptable results since notches overestimate the rejection capability of the filter. Furthermore, the losses within
+{\color{red}Initial considered criteria include the mean value of the stopband rejection which yields unacceptable results since notches 
+overestimate the rejection capability of the filter.} 
+% Furthermore, the losses within
 % the passband are not considered and might be excessive for excessively wide transitions widths introduced for filters with few coefficients.
-Our criterion to compute the filter rejection considers
+Our final criterion to compute the filter rejection considers
 % r2.8 et r2.2 r2.3
 the {\color{red}minimal} rejection within the stopband, to which the {\color{red}sum of the absolute values
 within the passband is subtracted to avoid filters with excessive ripples, normalized to the
@@ -460,7 +461,7 @@
 % The Gurobi (\url{www.gurobi.com}) optimization software used to solve this quadratic
 % model is able to linearize the model provided as is. This model
 % has $O(np)$ variables and $O(n)$ constraints.}
-However the problem remains quadratic at this stage since in the constraint~\ref{eq:areadef2}
+The problem remains quadratic at this stage since in the constraint~\ref{eq:areadef2}
 we multiply
 $\delta_{ij}$ and $\pi_i^-$. However, since $\delta_{ij}$ is a binary variable we can
 linearise linearize this multiplication. The following formula shows how to linearize
@@ -1109,7 +1110,7 @@
 same coefficient set and we compare the resource consumption, having checked that
 the transfer functions are indeed the same with both implementations.
 Table~\ref{tbl:xilinx_resources} exhibits the results.
-The FIR Compiler never use BRAM while our filter implementation uses one block. This difference
+The FIR Compiler never uses BRAM while our filter implementation uses one block. This difference
 is explained be our wish to have a dynamically reconfigurable FIR filter whose
 coefficients can be updated from the processing system without having to update the FPGA design.
 With the FIR compiler, the coefficients are defined during the FPGA design so that
@@ -76,8 +76,19 @@
 \documentclass[a4paper]{article}
 \usepackage{fullpage,graphicx,amsmath, subcaption}
 \begin{document}
-{\bf Reviewer: 1}
+\begin{center}
+{\bf\Large 
+Rebuttal letter to the review of the manuscript entitled
  
+``Filter optimization for real time digital processing of radiofrequency
+signals: application to oscillator metrology''
+}
+
+by A. Hugeat \& al.
+\end{center}
+
+\section*{Reviewer: 1}
+
 %Comments to the Author
 %In general, the language/grammar is adequate.
  
  
  
@@ -119,14 +130,15 @@
 for examination online.
 }
  
-To compare the performance of our FIR filters and the performance of device
-manufacturers generic filter, we have added a paragraph and a table at the
+We have compared the performance of our FIR filters and the performance of device
+manufacturers generic filter: we have added a paragraph and a table at the
 end of experiments section. We compare the resources consumption with the same
-FIR coefficients set.
+FIR coefficients set, demonstrating that the transfer functions match and that
+resources are somewhat similar despite different assumptions (Xilinx sets coefficients
+upon synthesis while we wish to be able to update taps without synthesis).
  
-{\bf
-Reviewer: 2
-}
+\noindent
+\section*{Reviewer: 2}
  
 %Comments to the Author
 %In the Manuscript, the Authors describe an optimization methodology for filter
@@ -159,7 +171,7 @@
 n = 1.
 }
  
-We have added on Figs 10--16 (now Fig 9(a)--(c)) the templates used to defined
+We have added on Figs 10--16 (now Fig 9(a)--(c)) the templates used to define
 the bandpass and the bandstop of the filter.
  
 % We are aware of this non equivalence but we think that difference is not due to
  
  
@@ -180,21 +192,21 @@
 % by this. So to improve the results, we can choose another criterion to be more
 % selective in passband but it is not the main objective of our article.
  
-We are aware of this equivalence but to limit this ripples in passband we need to
-enforce the criterion in passband. If we takes a strong constraint like the sum of
-absolute values in passband. This criterion si too selective because it considers
-all bin on passband while on stopband we consider only the bin with the minimal
-rejection. The figure~\ref{fig:letter_sum_criterion} exhibits the results with this
-criterion for the case MAX/1000. With this criterion, the solver find an optimal
-solution with only two filters in expend of the resource consumption.
+We are aware of this difference between the cascaded and monolithic filters but
+we consider that limiting the ripples in passband is more a matter of enforcing some
+selection criteria rather than being intrinsic to cascading filters. Selecting
+a strong constraint such as the sum of absolute values in the passband is too selective 
+because it considers all frequency bins in the passband while the stopband criterion is
+limited to a single bin at which rejection is poorest. Fig.~\ref{fig:letter_sum_criterion} 
+exhibits the results with this
+criterion for the case MAX/1000. With this criterion, the solver finds an optimal
+solution with only two filters. % in expend of the resource consumption.
  
-
-
-If we relax a little the criterion on passband with taking only the maximum absolute
-value, we will penalize the ripple peak on passband. The figure~\ref{fig:letter_max_criterion}
+Relaxing the criterion in the passband by considering only the maximum absolute
+value, we penalize the ripple peak in the passband. Fig.~\ref{fig:letter_max_criterion}
 shows the results for the case MAX/1000. There as almost no difference with the
 article results. Indeed the only little change are on the case $i = 4$ and $i = 5$
-which they have some minor differences on coefficients choices.
+which exhibit some minor differences on coefficients choices.
  
 \begin{figure}[h!tb]
   \centering
  
@@ -210,13 +222,19 @@
   \end{subfigure}
 \end{figure}
  
-Finally, if we ponder the maximum absolute on passband, we should improve the result.
-We have arbitrary pondered by 5 the maximum. Even with this weighting, the solver
-choose the same coefficient set.
+Finally, if we weight the maximum absolute value in the passband, we might improve the result.
+We have arbitrary weighted by a factor of 5 the maximum of the absolute value in the passband. 
+Even with this weighting, the solver chooses the same coefficient set.
  
-To conclude, find a better criterion to avoid the ripples on the passband is difficult.
-In this article we are focused on the methodology so even if our criterion could
-be improved, our methodology still the same and it works independently of rejection criterion.
+To conclude, finding a better criterion to avoid the ripples in the passband is challenging.
+In this article we focus on the methodology, so even if our criterion could
+be improved, our methodology still remains and works independently of rejection criterion.
+The averaging of the absolute values is the passband is a matter of having consistent units
+between the bandstop and banspass criteria: the bandstop criterion is the bin with poorest
+rejection so in units of dB/Hz. Using a bandpass criterion of the sum of absolute values
+in all bins would be a unit of dB: normalizing by the number of bins, equivalent to averaging
+by dividing by the number of bins, brings back a criterion in dB/Hz consistent with the
+former value.
  
 % %Peut etre refaire une serie de simulation dans lesquelles on impose une coupure
 % %non pas entre 40 et 60\% mais entre 50 et 60\% pour demontrer que l'outil s'adapte
@@ -244,8 +262,8 @@
 and in the results that are obtained and has to be reconsidered.
 }
  
-See above: Choose a criterion is difficult and depending on the context. The main
-contribution on this paper is the methodology not the criterion to quantify the
+See above: choosing a criterion is challenging and dependent on the context. The main
+contribution on this paper is the methodology rather than the criterion to quantify the
 rejection.
  
 % The manuscript erroneously stated that we considered the mean of the absolute
@@ -320,7 +338,8 @@
 Fig. 5 can be removed.
 }
  
-Juste mettre une phrase pour dire que la mean ne donnait pas de bons résultats
+We have kept a sentence stating our initial line of thought to avoid readers from performing
+the same mistake, but have removed the associated figure as requested.
  
 {\bf
 - Page 3, line 55: ``maximum rejection'' is not compatible with fig. 4.             % r2.8  - fait
  
@@ -351,10 +370,10 @@
  
 The first model is non-quadratic but when we introduce the $p$ configurations,
 we can estimate the function $F$ by computing
-the rejection for each configuration, so the model become quadratic because we have
+the rejection for each configuration, so the model becomes quadratic because we have
 some multiplication between variables. With the definition of $\delta_{ij}$ we can
-replace the multiplication between variables by multiplication with binary variable and
-this one can be linearise as follow:\\
+replace the multiplication between variables by multiplication with binary variables which
+can be linearised as follows:\\
 $y$ is a binary variable \\
 $x$ is a real variable bounded by $X^{max}$ \\
 \begin{equation*}
@@ -368,8 +387,9 @@
   \end{split}
   \right .
 \end{equation*}
-Gurobi does the linearization so we don't explain this step to keep the model more
-simple. However, to improve the transformation explanation we have rewrote the
+as explained now in the manuscript. Gurobi does the linearization so we do not explain 
+this step to keep the model more
+simple. However, to improve the transformation explanation we have rewritten the
 paragraph ``This model is non-linear and even non-quadratic...''.
  
 % JMF : il faudra mettre une phrase qui explique, ca en lisant cette reponse dans l'article
  
  
@@ -393,13 +413,15 @@
 {\bf
 - Captions of figure and tables are too minimal.                                  % r2.14
 }
-We have change the captions of tables and figures.
  
+Captions of figures were expanded to make the description easier to grasp by the reader
+
 {\bf
 - Figures can be grouped: fig. 10-12 can be grouped as three subplots (a, b, c)   % r2.15 - fait
 of a single figure. Same for fig. 13-16.
 }
-We add two sub figure to group the fig.10-12 and fig. 13-16
+
+We have grouped figures 10--12 and 13--16 as two sets of sub-figures.
  
 {\bf
 - Please increase the number of averages for the spectrum. Currently the noise    % r2.16 - fait
...	...	@@ -292,10 +292,11 @@
292	292
293	293	In the transition band, the behavior of the filter is left free, we only {\color{red}define} the passband and the stopband characteristics.
294	294	% r2.7
295		-% Our initial criterion considered the mean value of the stopband rejection, as shown in figure~\ref{fig:mean_criterion}. This criterion
296		-% yields unacceptable results since notches overestimate the rejection capability of the filter. Furthermore, the losses within
	295	+{\color{red}Initial considered criteria include the mean value of the stopband rejection which yields unacceptable results since notches
	296	+overestimate the rejection capability of the filter.}
	297	+% Furthermore, the losses within
297	298	% the passband are not considered and might be excessive for excessively wide transitions widths introduced for filters with few coefficients.
298		-Our criterion to compute the filter rejection considers
	299	+Our final criterion to compute the filter rejection considers
299	300	% r2.8 et r2.2 r2.3
300	301	the {\color{red}minimal} rejection within the stopband, to which the {\color{red}sum of the absolute values
301	302	within the passband is subtracted to avoid filters with excessive ripples, normalized to the
...	...	@@ -460,7 +461,7 @@
460	461	% The Gurobi (\url{www.gurobi.com}) optimization software used to solve this quadratic
461	462	% model is able to linearize the model provided as is. This model
462	463	% has $O(np)$ variables and $O(n)$ constraints.}
463		-However the problem remains quadratic at this stage since in the constraint~\ref{eq:areadef2}
	464	+The problem remains quadratic at this stage since in the constraint~\ref{eq:areadef2}
464	465	we multiply
465	466	$\delta_{ij}$ and $\pi_i^-$. However, since $\delta_{ij}$ is a binary variable we can
466	467	linearise linearize this multiplication. The following formula shows how to linearize
...	...	@@ -1109,7 +1110,7 @@
1109	1110	same coefficient set and we compare the resource consumption, having checked that
1110	1111	the transfer functions are indeed the same with both implementations.
1111	1112	Table~\ref{tbl:xilinx_resources} exhibits the results.
1112		-The FIR Compiler never use BRAM while our filter implementation uses one block. This difference
	1113	+The FIR Compiler never uses BRAM while our filter implementation uses one block. This difference
1113	1114	is explained be our wish to have a dynamically reconfigurable FIR filter whose
1114	1115	coefficients can be updated from the processing system without having to update the FPGA design.
1115	1116	With the FIR compiler, the coefficients are defined during the FPGA design so that
...	...	@@ -76,8 +76,19 @@
76	76	\documentclass[a4paper]{article}
77	77	\usepackage{fullpage,graphicx,amsmath, subcaption}
78	78	\begin{document}
79		-{\bf Reviewer: 1}
	79	+\begin{center}
	80	+{\bf\Large
	81	+Rebuttal letter to the review of the manuscript entitled
80	82
	83	+``Filter optimization for real time digital processing of radiofrequency
	84	+signals: application to oscillator metrology''
	85	+}
	86	+
	87	+by A. Hugeat \& al.
	88	+\end{center}
	89	+
	90	+\section*{Reviewer: 1}
	91	+
81	92	%Comments to the Author
82	93	%In general, the language/grammar is adequate.
83	94
84	95
85	96
...	...	@@ -119,14 +130,15 @@
119	130	for examination online.
120	131	}
121	132
122		-To compare the performance of our FIR filters and the performance of device
123		-manufacturers generic filter, we have added a paragraph and a table at the
	133	+We have compared the performance of our FIR filters and the performance of device
	134	+manufacturers generic filter: we have added a paragraph and a table at the
124	135	end of experiments section. We compare the resources consumption with the same
125		-FIR coefficients set.
	136	+FIR coefficients set, demonstrating that the transfer functions match and that
	137	+resources are somewhat similar despite different assumptions (Xilinx sets coefficients
	138	+upon synthesis while we wish to be able to update taps without synthesis).
126	139
127		-{\bf
128		-Reviewer: 2
129		-}
	140	+\noindent
	141	+\section*{Reviewer: 2}
130	142
131	143	%Comments to the Author
132	144	%In the Manuscript, the Authors describe an optimization methodology for filter
...	...	@@ -159,7 +171,7 @@
159	171	n = 1.
160	172	}
161	173
162		-We have added on Figs 10--16 (now Fig 9(a)--(c)) the templates used to defined
	174	+We have added on Figs 10--16 (now Fig 9(a)--(c)) the templates used to define
163	175	the bandpass and the bandstop of the filter.
164	176
165	177	% We are aware of this non equivalence but we think that difference is not due to
166	178
167	179
...	...	@@ -180,21 +192,21 @@
180	192	% by this. So to improve the results, we can choose another criterion to be more
181	193	% selective in passband but it is not the main objective of our article.
182	194
183		-We are aware of this equivalence but to limit this ripples in passband we need to
184		-enforce the criterion in passband. If we takes a strong constraint like the sum of
185		-absolute values in passband. This criterion si too selective because it considers
186		-all bin on passband while on stopband we consider only the bin with the minimal
187		-rejection. The figure~\ref{fig:letter_sum_criterion} exhibits the results with this
188		-criterion for the case MAX/1000. With this criterion, the solver find an optimal
189		-solution with only two filters in expend of the resource consumption.
	195	+We are aware of this difference between the cascaded and monolithic filters but
	196	+we consider that limiting the ripples in passband is more a matter of enforcing some
	197	+selection criteria rather than being intrinsic to cascading filters. Selecting
	198	+a strong constraint such as the sum of absolute values in the passband is too selective
	199	+because it considers all frequency bins in the passband while the stopband criterion is
	200	+limited to a single bin at which rejection is poorest. Fig.~\ref{fig:letter_sum_criterion}
	201	+exhibits the results with this
	202	+criterion for the case MAX/1000. With this criterion, the solver finds an optimal
	203	+solution with only two filters. % in expend of the resource consumption.
190	204
191		-
192		-
193		-If we relax a little the criterion on passband with taking only the maximum absolute
194		-value, we will penalize the ripple peak on passband. The figure~\ref{fig:letter_max_criterion}
	205	+Relaxing the criterion in the passband by considering only the maximum absolute
	206	+value, we penalize the ripple peak in the passband. Fig.~\ref{fig:letter_max_criterion}
195	207	shows the results for the case MAX/1000. There as almost no difference with the
196	208	article results. Indeed the only little change are on the case $i = 4$ and $i = 5$
197		-which they have some minor differences on coefficients choices.
	209	+which exhibit some minor differences on coefficients choices.
198	210
199	211	\begin{figure}[h!tb]
200	212	\centering
201	213
...	...	@@ -210,13 +222,19 @@
210	222	\end{subfigure}
211	223	\end{figure}
212	224
213		-Finally, if we ponder the maximum absolute on passband, we should improve the result.
214		-We have arbitrary pondered by 5 the maximum. Even with this weighting, the solver
215		-choose the same coefficient set.
	225	+Finally, if we weight the maximum absolute value in the passband, we might improve the result.
	226	+We have arbitrary weighted by a factor of 5 the maximum of the absolute value in the passband.
	227	+Even with this weighting, the solver chooses the same coefficient set.
216	228
217		-To conclude, find a better criterion to avoid the ripples on the passband is difficult.
218		-In this article we are focused on the methodology so even if our criterion could
219		-be improved, our methodology still the same and it works independently of rejection criterion.
	229	+To conclude, finding a better criterion to avoid the ripples in the passband is challenging.
	230	+In this article we focus on the methodology, so even if our criterion could
	231	+be improved, our methodology still remains and works independently of rejection criterion.
	232	+The averaging of the absolute values is the passband is a matter of having consistent units
	233	+between the bandstop and banspass criteria: the bandstop criterion is the bin with poorest
	234	+rejection so in units of dB/Hz. Using a bandpass criterion of the sum of absolute values
	235	+in all bins would be a unit of dB: normalizing by the number of bins, equivalent to averaging
	236	+by dividing by the number of bins, brings back a criterion in dB/Hz consistent with the
	237	+former value.
220	238
221	239	% %Peut etre refaire une serie de simulation dans lesquelles on impose une coupure
222	240	% %non pas entre 40 et 60\% mais entre 50 et 60\% pour demontrer que l'outil s'adapte
...	...	@@ -244,8 +262,8 @@
244	262	and in the results that are obtained and has to be reconsidered.
245	263	}
246	264
247		-See above: Choose a criterion is difficult and depending on the context. The main
248		-contribution on this paper is the methodology not the criterion to quantify the
	265	+See above: choosing a criterion is challenging and dependent on the context. The main
	266	+contribution on this paper is the methodology rather than the criterion to quantify the
249	267	rejection.
250	268
251	269	% The manuscript erroneously stated that we considered the mean of the absolute
...	...	@@ -320,7 +338,8 @@
320	338	Fig. 5 can be removed.
321	339	}
322	340
323		-Juste mettre une phrase pour dire que la mean ne donnait pas de bons résultats
	341	+We have kept a sentence stating our initial line of thought to avoid readers from performing
	342	+the same mistake, but have removed the associated figure as requested.
324	343
325	344	{\bf
326	345	- Page 3, line 55: ``maximum rejection'' is not compatible with fig. 4. % r2.8 - fait
327	346
...	...	@@ -351,10 +370,10 @@
351	370
352	371	The first model is non-quadratic but when we introduce the $p$ configurations,
353	372	we can estimate the function $F$ by computing
354		-the rejection for each configuration, so the model become quadratic because we have
	373	+the rejection for each configuration, so the model becomes quadratic because we have
355	374	some multiplication between variables. With the definition of $\delta_{ij}$ we can
356		-replace the multiplication between variables by multiplication with binary variable and
357		-this one can be linearise as follow:\\
	375	+replace the multiplication between variables by multiplication with binary variables which
	376	+can be linearised as follows:\\
358	377	$y$ is a binary variable \\
359	378	$x$ is a real variable bounded by $X^{max}$ \\
360	379	\begin{equation*}
...	...	@@ -368,8 +387,9 @@
368	387	\end{split}
369	388	\right .
370	389	\end{equation*}
371		-Gurobi does the linearization so we don't explain this step to keep the model more
372		-simple. However, to improve the transformation explanation we have rewrote the
	390	+as explained now in the manuscript. Gurobi does the linearization so we do not explain
	391	+this step to keep the model more
	392	+simple. However, to improve the transformation explanation we have rewritten the
373	393	paragraph ``This model is non-linear and even non-quadratic...''.
374	394
375	395	% JMF : il faudra mettre une phrase qui explique, ca en lisant cette reponse dans l'article
376	396
377	397
...	...	@@ -393,13 +413,15 @@
393	413	{\bf
394	414	- Captions of figure and tables are too minimal. % r2.14
395	415	}
396		-We have change the captions of tables and figures.
397	416
	417	+Captions of figures were expanded to make the description easier to grasp by the reader
	418	+
398	419	{\bf
399	420	- Figures can be grouped: fig. 10-12 can be grouped as three subplots (a, b, c) % r2.15 - fait
400	421	of a single figure. Same for fig. 13-16.
401	422	}
402		-We add two sub figure to group the fig.10-12 and fig. 13-16
	423	+
	424	+We have grouped figures 10--12 and 13--16 as two sets of sub-figures.
403	425
404	426	{\bf
405	427	- Please increase the number of averages for the spectrum. Currently the noise % r2.16 - fait