Arthur HUGEAT · Arthur HUGEAT
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.gitignore
Makefile
ifcs2018_journal.tex
ifcs2018_journal_reponse.tex
images/cascaded_criterion.pdf
images/colored_custom_criterion.pdf
images/colored_mean_criterion.pdf
images/max_1000.pdf
images/max_1500.pdf
images/max_500.pdf
images/min_100.pdf
images/min_40.pdf
images/min_60.pdf
images/min_80.pdf
images/rejection_pyramid.pdf
images/zero_values.pdf
tuffc.pdf
@@ -24,4 +24,12 @@ ifcs2018_journal.log
 ifcs2018_journal.out
 ifcs2018_journal.pdf
  
+ifcs2018_journal_reponse.aux
+ifcs2018_journal_reponse.log
+ifcs2018_journal_reponse.pdf
+
+cover.aux
+cover.log
+cover.pdf
+
 *.bak
@@ -34,6 +34,10 @@ $(TARGET)_journal: $(TARGET)_journal.tex references.bib biblio.bib
 	$(TEX) $@.tex
 	$(TEX) $@.tex
  
+$(TARGET)_journal_reponse: $(TARGET)_journal_reponse.tex references.bib biblio.bib
+	$(TEX) $@.tex
+	$(TEX) $@.tex
+
 clean:
 	rm -f $(TARGET)_abstract.aux $(TARGET)_abstract.log $(TARGET)_abstract.out $(TARGET)_abstract.bbl $(TARGET)_abstract.blg
 	rm -f $(TARGET)_poster.aux $(TARGET)_poster.log $(TARGET)_poster.out
@@ -23,6 +23,8 @@
 \usetikzlibrary{positioning,fit}
 \usepackage{multirow}
 \usepackage{scalefnt}
+\usepackage{caption}
+\usepackage{subcaption}
  
 % correct bad hyphenation here
 \hyphenation{op-tical net-works semi-conduc-tor}
@@ -35,8 +37,8 @@ to oscillator metrology}
  
 \author{\IEEEauthorblockN{A. Hugeat\IEEEauthorrefmark{1}\IEEEauthorrefmark{2}, J. Bernard\IEEEauthorrefmark{2},
 G. Goavec-M\'erou\IEEEauthorrefmark{1},
-P.-Y. Bourgeois\IEEEauthorrefmark{1}, J.-M. Friedt\IEEEauthorrefmark{1}}
-\IEEEauthorblockA{\IEEEauthorrefmark{1}FEMTO-ST, Time \& Frequency department, Besan\c con, France }
+P.-Y. Bourgeois\IEEEauthorrefmark{1}, J.-M. Friedt\IEEEauthorrefmark{1}}\\
+\IEEEauthorblockA{\IEEEauthorrefmark{1}FEMTO-ST, Time \& Frequency department, Besan\c con, France }\\
 \IEEEauthorblockA{\IEEEauthorrefmark{2}FEMTO-ST, Computer Science department DISC, Besan\c con, France \\
 Email: \{pyb2,jmfriedt\}@femto-st.fr}
 }
@@ -280,17 +282,20 @@ the stopband the last 40\%, allowing 20\% transition width.}
 \end{figure}
  
 In the transition band, the behavior of the filter is left free, we only care about the passband and the stopband characteristics.
-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
-the passband are not considered and might be excessive for excessively wide transitions widths introduced for filters with few coefficients.
-Such biases are compensated for by the second considered criterion which is based on computing the maximum rejection within the stopband minus the mean of the absolute value of passband rejection. With this criterion, the results are significantly improved as shown in figure~\ref{fig:custom_criterion} and meet the expected rejection capability of low pass filters.
-
-\begin{figure}
-\centering
-\includegraphics[width=\linewidth]{images/colored_mean_criterion}
-\caption{Mean stopband rejection criterion comparison between monolithic filter and cascaded filters}
-\label{fig:mean_criterion}
-\end{figure}
+% 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
+% 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 takes
+% r2.8 et r2.2 r2.3
+the maximum magnitude within the stopband minus the sum of the absolute value of passband rejection. With this criterion, we meet the expected rejection capability of low pass filters as shown in figure~\ref{fig:custom_criterion}.
+
+% \begin{figure}
+% \centering
+% \includegraphics[width=\linewidth]{images/colored_mean_criterion}
+% \caption{Mean stopband rejection criterion comparison between monolithic filter and cascaded filters}
+% \label{fig:mean_criterion}
+% \end{figure}
  
 \begin{figure}
 \centering
@@ -324,9 +329,11 @@ the previous relation is no longer valid as illustrated on figure~\ref{fig:sum_r
 are two different filters with maximums and notches not located at the same frequency offsets.
 Hence when summing the transfer functions, the resulting rejection shown as the dashed yellow line is improved
 with respect to a basic sum of the rejection criteria shown as a the dotted yellow line.
-Thus, estimating the rejection of filter cascades is more complex than takin the sum of all the rejection
+% r2.9
+Thus, estimating the rejection of filter cascades is more complex than taking the sum of all the rejection
 criteria of each filter. However since the this sum underestimates the rejection capability of the cascade,
-this upper bound is considered as a pessimistic and acceptable criterion for deciding on the suitability
+% r2.10
+this upper bound is considered as a conservative and acceptable criterion for deciding on the suitability
 of the filter cascade to meet design criteria.
  
 \begin{figure}
@@ -336,8 +343,14 @@ of the filter cascade to meet design criteria.
 \label{fig:sum_rejection}
 \end{figure}
  
+% r2.6
+Finally in our case, we consider that the input signal are fully known. So the
+resolution of the data stream are fixed and still the same for all experiments
+in this paper.
+
 Based on this analysis, we address the estimate of resource consumption (called
-silicon area -- in the case of FPGAs meaning processing cells) as a function of
+% r2.11
+silicon area -- in the case of FPGAs this means processing cells) as a function of
 filter characteristics. As a reminder, we do not aim at matching actual hardware
 configuration but consider an arbitrary silicon area occupied by each processing function,
 and will assess after synthesis the adequation of this arbitrary unit with actual
@@ -383,7 +396,12 @@ Finally, equation~\ref{eq:init} gives the number of bits of the global input.
  
 This model is non-linear and even non-quadratic, as $F$ does not have a known
 linear or quadratic expression. We introduce $p$ FIR configurations
-$(C_{ij}, \pi_{ij}^C), 1 \leq j \leq p$ that are constants. We define binary
+$(C_{ij}, \pi_{ij}^C), 1 \leq j \leq p$ that are constants.
+% r2.12
+This variable must be defined by the user, it represent the number of different
+set of coefficients generated (for memory, we use \texttt{firls} and \texttt{fir1}
+functions from GNU Octave).
+We define binary
 variable $\delta_{ij}$ that has value 1 if stage~$i$ is in configuration~$j$
 and 0 otherwise. The new equations are as follows:
  
@@ -398,7 +416,10 @@ Equations \ref{eq:areadef2}, \ref{eq:rejectiondef2} and \ref{eq:bits2} replace
 respectively equations \ref{eq:areadef}, \ref{eq:rejectiondef} and \ref{eq:bits}.
 Equation~\ref{eq:config} states that for each stage, a single configuration is chosen at most.
  
-This modified model is quadratic, and it can be linearised if necessary. The Gurobi
+% r2.13
+This modified model is quadratic since we multiply two variables in the
+equation~\ref{eq:areadef2} ($\delta_{ij}$ by $\pi_{ij}^-$) but it can be linearised if necessary.
+The Gurobi
 (\url{www.gurobi.com}) optimization software is used to solve this quadratic
 model, and since Gurobi is able to linearize, the model is left as is. This model
 has $O(np)$ variables and $O(n)$ constraints.
@@ -602,25 +623,48 @@ Figure~\ref{fig:max_500_result} shows the rejection of the different configurati
 Figure~\ref{fig:max_1000_result} shows the rejection of the different configurations in the case of MAX/1000.
 Figure~\ref{fig:max_1500_result} shows the rejection of the different configurations in the case of MAX/1500.
  
+% \begin{figure}
+% \centering
+% \includegraphics[width=\linewidth]{images/max_500}
+% \caption{Signal spectrum for MAX/500}
+% \label{fig:max_500_result}
+% \end{figure}
+%
+% \begin{figure}
+% \centering
+% \includegraphics[width=\linewidth]{images/max_1000}
+% \caption{Signal spectrum for MAX/1000}
+% \label{fig:max_1000_result}
+% \end{figure}
+%
+% \begin{figure}
+% \centering
+% \includegraphics[width=\linewidth]{images/max_1500}
+% \caption{Signal spectrum for MAX/1500}
+% \label{fig:max_1500_result}
+% \end{figure}
+
+% r2.14 et r2.15 et r2.16
 \begin{figure}
-\centering
-\includegraphics[width=\linewidth]{images/max_500}
-\caption{Signal spectrum for MAX/500}
-\label{fig:max_500_result}
-\end{figure}
-
-\begin{figure}
-\centering
-\includegraphics[width=\linewidth]{images/max_1000}
-\caption{Signal spectrum for MAX/1000}
-\label{fig:max_1000_result}
-\end{figure}
-
-\begin{figure}
-\centering
-\includegraphics[width=\linewidth]{images/max_1500}
-\caption{Signal spectrum for MAX/1500}
-\label{fig:max_1500_result}
+  \centering
+  \begin{subfigure}{\linewidth}
+    \includegraphics[width=\linewidth]{images/max_500}
+    \caption{Signal spectrum for MAX/500}
+    \label{fig:max_500_result}
+  \end{subfigure}
+
+  \begin{subfigure}{\linewidth}
+    \includegraphics[width=\linewidth]{images/max_1000}
+    \caption{Signal spectrum for MAX/1000}
+    \label{fig:max_1000_result}
+  \end{subfigure}
+
+  \begin{subfigure}{\linewidth}
+    \includegraphics[width=\linewidth]{images/max_1500}
+    \caption{Signal spectrum for MAX/1500}
+    \label{fig:max_1500_result}
+  \end{subfigure}
+  \caption{Signal spectrum of each experimental configurations MAX/500, MAX/1000 and MAX/1500}
 \end{figure}
  
 In all cases, we observe that the actual rejection is close to the rejection computed by the solver.
@@ -827,32 +871,61 @@ Figure~\ref{fig:min_60} shows the rejection of the different configurations in t
 Figure~\ref{fig:min_80} shows the rejection of the different configurations in the case of MIN/80.
 Figure~\ref{fig:min_100} shows the rejection of the different configurations in the case of MIN/100.
  
+% \begin{figure}
+% \centering
+% \includegraphics[width=\linewidth]{images/min_40}
+% \caption{Signal spectrum for MIN/40}
+% \label{fig:min_40}
+% \end{figure}
+%
+% \begin{figure}
+% \centering
+% \includegraphics[width=\linewidth]{images/min_60}
+% \caption{Signal spectrum for MIN/60}
+% \label{fig:min_60}
+% \end{figure}
+%
+% \begin{figure}
+% \centering
+% \includegraphics[width=\linewidth]{images/min_80}
+% \caption{Signal spectrum for MIN/80}
+% \label{fig:min_80}
+% \end{figure}
+%
+% \begin{figure}
+% \centering
+% \includegraphics[width=\linewidth]{images/min_100}
+% \caption{Signal spectrum for MIN/100}
+% \label{fig:min_100}
+% \end{figure}
+
+% r2.14 et r2.15 et r2.16
 \begin{figure}
-\centering
-\includegraphics[width=\linewidth]{images/min_40}
-\caption{Signal spectrum for MIN/40}
-\label{fig:min_40}
-\end{figure}
-
-\begin{figure}
-\centering
-\includegraphics[width=\linewidth]{images/min_60}
-\caption{Signal spectrum for MIN/60}
-\label{fig:min_60}
-\end{figure}
-
-\begin{figure}
-\centering
-\includegraphics[width=\linewidth]{images/min_80}
-\caption{Signal spectrum for MIN/80}
-\label{fig:min_80}
-\end{figure}
-
-\begin{figure}
-\centering
-\includegraphics[width=\linewidth]{images/min_100}
-\caption{Signal spectrum for MIN/100}
-\label{fig:min_100}
+  \centering
+  \begin{subfigure}{\linewidth}
+    \includegraphics[width=\linewidth]{images/min_40}
+    \caption{Signal spectrum for MIN/40}
+    \label{fig:min_40}
+  \end{subfigure}
+
+  \begin{subfigure}{\linewidth}
+    \includegraphics[width=\linewidth]{images/min_60}
+    \caption{Signal spectrum for MIN/60}
+    \label{fig:min_60}
+  \end{subfigure}
+
+  \begin{subfigure}{\linewidth}
+    \includegraphics[width=\linewidth]{images/min_80}
+    \caption{Signal spectrum for MIN/80}
+    \label{fig:min_80}
+  \end{subfigure}
+
+  \begin{subfigure}{\linewidth}
+    \includegraphics[width=\linewidth]{images/min_100}
+    \caption{Signal spectrum for MIN/100}
+    \label{fig:min_100}
+  \end{subfigure}
+  \caption{Signal spectrum of each experimental configurations MIN/40, MIN/60, MIN/80 and MIN/100}
 \end{figure}
  
 We observe that all rejections given by the quadratic solver are close to the experimentally
 %Minor Revision - TUFFC-09469-2019
-%Transactions on Ultrasonics, Ferroelectrics, and Frequency 
+%Transactions on Ultrasonics, Ferroelectrics, and Frequency
 %Control (July 23, 2019 9:29 PM)
-%To: arthur.hugeat@femto-st.fr, julien.bernard@femto-st.fr, 
-%gwenhael.goavec@femto-st.fr, pyb2@femto-st.fr, pierre-yves.bourgeois@femto-st.fr, 
+%To: arthur.hugeat@femto-st.fr, julien.bernard@femto-st.fr,
+%gwenhael.goavec@femto-st.fr, pyb2@femto-st.fr, pierre-yves.bourgeois@femto-st.fr,
 %jmfriedt@femto-st.fr
 %CC: giorgio.santarelli@institutoptique.fr, lewin@ece.drexel.edu
 %
@@ -12,56 +12,56 @@
 %
 %MANUSCRIPT NO. TUFFC-09469-2019
 %MANUSCRIPT TYPE: Papers
-%TITLE: Filter optimization for real time digital processing of radiofrequency 
+%TITLE: Filter optimization for real time digital processing of radiofrequency
 %signals: application to oscillator metrology
-%AUTHOR(S): HUGEAT, Arthur; BERNARD, Julien; Goavec-Mérou, Gwenhaël; Bourgeois, 
+%AUTHOR(S): HUGEAT, Arthur; BERNARD, Julien; Goavec-Mérou, Gwenhaël; Bourgeois,
 %Pierre-Yves; Friedt, Jean-Michel
 %
-%has been reviewed and it has been suggested that it be accepted for publication 
-%after minor revisions. In your revision, you must respond to the reviewer’s 
+%has been reviewed and it has been suggested that it be accepted for publication
+%after minor revisions. In your revision, you must respond to the reviewer’s
 %comments at the end of this e-mail or attached.
 %
-%Your revised manuscript must be submitted within the next THREE WEEKS. If you 
-%are not able to submit your manuscript in this time frame, you must contact the 
+%Your revised manuscript must be submitted within the next THREE WEEKS. If you
+%are not able to submit your manuscript in this time frame, you must contact the
 %Editor in Chief (Peter Lewin, lewinpa@drexel.edu).
 %
-%Please resubmit your revised manuscript to the Transactions on Ultrasonics, 
-%Ferroelectrics, and Frequency Control Manuscript Central website at 
-%http://mc.manuscriptcentral.com/tuffc-ieee. From the “Author Center” select 
-%“Manuscripts with Decisions” and under the appropriate manuscript ID select 
+%Please resubmit your revised manuscript to the Transactions on Ultrasonics,
+%Ferroelectrics, and Frequency Control Manuscript Central website at
+%http://mc.manuscriptcentral.com/tuffc-ieee. From the “Author Center” select
+%“Manuscripts with Decisions” and under the appropriate manuscript ID select
 %“create a revision”.
 %
 %To expedite the review of your resubmission:
 %
-%(1) Include or attach a point by point response to reviewer’s comments and 
-%detail all changes made in your manuscript under “Response to Decision Letter”. 
-%Failure to address reviewers comments can still lead to a rejection of your 
+%(1) Include or attach a point by point response to reviewer’s comments and
+%detail all changes made in your manuscript under “Response to Decision Letter”.
+%Failure to address reviewers comments can still lead to a rejection of your
 %manuscript.
-%(2) Submit a PDF of the revised manuscript using the “Formatted (Double Column) 
-%Main File - PDF Document Only” file type with all changes highlighted in yellow 
+%(2) Submit a PDF of the revised manuscript using the “Formatted (Double Column)
+%Main File - PDF Document Only” file type with all changes highlighted in yellow
 %under “File Upload”.
-%(3) Original TeX, LaTeX, or Microsoft Word file of the final manuscript as 
+%(3) Original TeX, LaTeX, or Microsoft Word file of the final manuscript as
 %Supporting Document.
-%(4) High quality source files of your figures in Word, Tiff, Postscript, 
-%EPS, Excel or Power Point (if figures are not already embedded in your source 
+%(4) High quality source files of your figures in Word, Tiff, Postscript,
+%EPS, Excel or Power Point (if figures are not already embedded in your source
 %file above) as Supporting Document.
 %(5) Author photos and biographies (papers only) as Supporting Document.
-%(6) Graphical Abstract to accompany your text abstract on IEEE Xplore (image, 
+%(6) Graphical Abstract to accompany your text abstract on IEEE Xplore (image,
 %animation, movie, or audio clip) uploaded as Multimedia.
 %
-%*Please make sure that all final files have unique file names in order for 
+%*Please make sure that all final files have unique file names in order for
 %them to be processed correctly by IEEE*
-%Please note that a PDF is NOT sufficient for publication, the PDF is used 
+%Please note that a PDF is NOT sufficient for publication, the PDF is used
 %for review.
 %
-%During the resubmission process if you do not see a confirmation screen and 
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+%receive a confirmation e-mail, your revised manuscript was not transmitted
 %to us and we will not be able to continue to process your manuscript.
 %
-%Please refer to the policies regarding the voluntary page charges and 
-%mandatory page charges in the "Guideline for Authors" at 
+%Please refer to the policies regarding the voluntary page charges and
+%mandatory page charges in the "Guideline for Authors" at
 %http://ieee-uffc.org/publications/transactions-on-uffc/information-for-authors
-%Note over-length charge of US$175 per page is applied for published pages in 
+%Note over-length charge of US$175 per page is applied for published pages in
 %excess of 8 pages.
 %
 %Sincerely,
@@ -82,22 +82,22 @@
 %In general, the language/grammar is adequate.
  
 {\bf
-On page 2,  "...allowing to save processing resource..." could be improved.
+On page 2,  "...allowing to save processing resource..." could be improved.       % r1.1
  
-On page 2, "... or thanks at a radiofrequency-grade..." isn't at all clear what 
+On page 2, "... or thanks at a radiofrequency-grade..." isn't at all clear what   % r1.2
 the author meant.
  
-One page 2, the whole paragraph "The first step of our approach is to model..." 
+One page 2, the whole paragraph "The first step of our approach is to model..."   % r1.3
 could be improved.
 }
  
 {\bf
-I appreciate that the authors attempted and document two optimizations: that 
-of maximum rejection ratio at fixed silicon area, as well as minimum silicon 
-area for a fixed minimum rejection ratio. For non-experts, it might be very 
-useful to compare the results of both optimization paths to the performance and 
-resource-utilization of generic low-pass filter gateware offered by device 
-manufacturers. I appreciate also that the authors have presented source code 
+I appreciate that the authors attempted and document two optimizations: that      % r1.4 - en attente des résultats
+of maximum rejection ratio at fixed silicon area, as well as minimum silicon
+area for a fixed minimum rejection ratio. For non-experts, it might be very
+useful to compare the results of both optimization paths to the performance and
+resource-utilization of generic low-pass filter gateware offered by device
+manufacturers. I appreciate also that the authors have presented source code
 for examination online.
 }
  
@@ -109,34 +109,34 @@ Reviewer: 2
 }
  
 %Comments to the Author
-%In the Manuscript, the Authors describe an optimization methodology for filter 
-%design to be used in phase noise metrology. The methodology is general and can 
-%be used for many aspects of the processing chain. In the Manuscript, the Authors 
-%focus on filtering and shifting while the other aspects, in particular decimation, 
-%will be considered in a future work. The optimization problem is modelled 
-%theoretically and then solved by means of a commercial software. The solutions 
-%are tested experimentally on the Redpitaya platform with synthetic and real 
-%white noises. Two cases are considered as a function of the number of filters: 
-%maximum rejection given a fixed amount of resources and minimum resource 
-%utilization given a fixed amount of rejection.  
-%The Authors find that filtering improves significantly when the number of 
-%filters increases. 
-%A lot of work has been done in generalizing and automating the procedure so 
-%that different approaches can be investigated quickly and efficiently. The 
-%results presented in the Manuscript seem to be just a case study based on 
-%the particular criterion chosen by the Authors. Different criteria, in 
-%general, could lead to different results and it is important to consider 
-%carefully the criterion adopted by the Authors, in order to check if it 
-%is adequate to compare the performance of filters and if multi-stage 
+%In the Manuscript, the Authors describe an optimization methodology for filter
+%design to be used in phase noise metrology. The methodology is general and can
+%be used for many aspects of the processing chain. In the Manuscript, the Authors
+%focus on filtering and shifting while the other aspects, in particular decimation,
+%will be considered in a future work. The optimization problem is modelled
+%theoretically and then solved by means of a commercial software. The solutions
+%are tested experimentally on the Redpitaya platform with synthetic and real
+%white noises. Two cases are considered as a function of the number of filters:
+%maximum rejection given a fixed amount of resources and minimum resource
+%utilization given a fixed amount of rejection.
+%The Authors find that filtering improves significantly when the number of
+%filters increases.
+%A lot of work has been done in generalizing and automating the procedure so
+%that different approaches can be investigated quickly and efficiently. The
+%results presented in the Manuscript seem to be just a case study based on
+%the particular criterion chosen by the Authors. Different criteria, in
+%general, could lead to different results and it is important to consider
+%carefully the criterion adopted by the Authors, in order to check if it
+%is adequate to compare the performance of filters and if multi-stage
 %filters are really superior than monolithic filters.
  
 {\bf
-By observing the results presented in fig. 10-16, it is clear that the 
-performances of multi-stage filters are obtained at the expense of their 
-selectivity and, in this sense, the filters presented in these figures 
-are not equivalent. For example, in Fig. 14, at the limit of the pass band, 
-the attenuation is almost 15 dB for n = 5, while it is not noticeable for 
-n = 1. 
+By observing the results presented in fig. 10-16, it is clear that the            % r2.1 - fait
+performances of multi-stage filters are obtained at the expense of their
+selectivity and, in this sense, the filters presented in these figures
+are not equivalent. For example, in Fig. 14, at the limit of the pass band,
+the attenuation is almost 15 dB for n = 5, while it is not noticeable for
+n = 1.
 }
  
 TODO : ajouter les gabarits
@@ -145,14 +145,16 @@ 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
 au critere qu'on lui impose, et que la coupure moins raide n'est pas intrinseque
 a la cascade de filtres.
+AH: Je finis les corrections, je poste l'article revu et pendant ce temps j'essaie de
+relancer des expérimentations. Si j'arrive à les finir à temps, je les intégrerai
  
 {\bf
-The reason is in the criterion that considers the average attenuation in 
-the pass band. This criterion does not take into account the maximum attenuation 
-in this region, which is a very important parameter for specifying a filter 
-and for evaluating its performance. For example, with this criterion, a 
-filter with 0.1 dB of ripple is considered equivalent to a filter with 
-10 dB of ripple. This point has a strong impact in the optimization process 
+The reason is in the criterion that considers the average attenuation in          % r2.2 - fait
+the pass band. This criterion does not take into account the maximum attenuation
+in this region, which is a very important parameter for specifying a filter
+and for evaluating its performance. For example, with this criterion, a
+filter with 0.1 dB of ripple is considered equivalent to a filter with
+10 dB of ripple. This point has a strong impact in the optimization process
 and in the results that are obtained and has to be reconsidered.
 }
  
@@ -160,54 +162,67 @@ Je ne pense pas que ca soit le cas : la somme des valeurs absolues des pertes
 dans la bande va defavoriser un filtre avec 10 dB de ripples. Il n'a pas compris que
 la bandpass s'arrete a 40\% de la bande, donc mettre le gabarit clarifierait ce point je
 pense
+AH: Il y avait une faute, j'avais mis "mean of absolute value" au lieu de "sum of absolute value". Je pense que je n'ai pas besoin de mettre plus de détail ?
  
 {\bf
-I strongly suggest to re-run the analysis with a criterion that takes also 
-into account the maximum allowed attenuation in pass band, for example by 
-fixing its value to a typical one, as it has been done for the transition 
-bandwidth. 
+I strongly suggest to re-run the analysis with a criterion that takes also        % r2.3 -fait
+into account the maximum allowed attenuation in pass band, for example by
+fixing its value to a typical one, as it has been done for the transition
+bandwidth.
 }
+AH: Il y avait une faute, j'avais mis "mean of absolute value" au lieu de "sum of absolute value". Je pense que je n'ai pas besoin de mettre plus de détail ?
  
 {\bf
-In addition, I suggest to address the following points:
-- Page 1, line 50: the Authors state that IIR have shorter impulse response 
+In addition, I suggest to address the following points:                           % r2.4
+- Page 1, line 50: the Authors state that IIR have shorter impulse response
 than FIR. This is not true in general. The sentence should be reconsidered.
 }
  
 J'aurais du dire ``lag'' au lieu de ``impulse response'' je pense
+AH: Je ne comprends pas trop ce qui ne va pas ici
  
 {\bf
-- Fig. 4: the Author should motivate in the text why it has been chosen 
-this transition bandwidth and if it is a typical requirement for phase-noise 
+- Fig. 4: the Author should motivate in the text why it has been chosen           % r2.5
+this transition bandwidth and if it is a typical requirement for phase-noise
 metrology.
-- The impact of the coefficient resolution is discussed. What about the 
-resolution of the data stream? Is it fixed? If so, which value has been 
-used in the analysis? If not, how is it changed with respect to the 
+}
+AH: Je ne sais pas comment justifier ça. Je dois dire que comme ça on peut éventuellement
+décimer par deux le flux ?
+
+{\bf
+- The impact of the coefficient resolution is discussed. What about the           % r2.6 - fait
+resolution of the data stream? Is it fixed? If so, which value has been
+used in the analysis? If not, how is it changed with respect to the
 coefficient resolution?
 }
  
 Pr\'eciser que le flux de donn\'ees en entr\'ees est de r\'esolution fixe
  
 {\bf
-- Page 3, line 47: the initial criterion can be omitted and, consequently, 
+- Page 3, line 47: the initial criterion can be omitted and, consequently,        % r2.7  - fait
 Fig. 5 can be removed.
-- Page 3, line 55: “maximum rejection” is not compatible with fig. 4. 
+- Page 3, line 55: “maximum rejection” is not compatible with fig. 4.             % r2.8  - fait
 It should be “minimum”
-- Page e, line 55, second column: “takin”
-- Page 3, line 58: “pessimistic” should be replaced with “conservative”
-- Page 4, line 17: “meaning” --> “this means”
-- Page 4, line 10: how $p$ is chosen? Which is the criterion used to choose 
+}
+AH: Je ne suis pas d'accord, le critère n'est pas le min de la rejection mais le max
+de la magnitude. J'ai corrigé en ce sens.
+
+{\bf
+- Page e, line 55, second column: “takin”                                         % r2.9  - fait
+- Page 3, line 58: “pessimistic” should be replaced with “conservative”           % r2.10 - fait
+- Page 4, line 17: “meaning” --> “this means”                                     % r2.11 - fait
+- Page 4, line 10: how $p$ is chosen? Which is the criterion used to choose       % r2.12 - fait
 these particular configurations? Are they chosen automatically?
-- Page 4, line 31: how does the delta function transform model from non-linear 
+- Page 4, line 31: how does the delta function transform model from non-linear    % r2.13 - fait
 and non-quadratic to a quadratic?
-- Captions of figure and tables are too minimal.
-- Figures can be grouped: fig. 10-12 can be grouped as three subplots (a, b, c) 
-of a single figure. Same for fig. 13-16. 
+- Captions of figure and tables are too minimal.                                  % r2.14
+- 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.
 }
  
 {\bf
-- Please increase the number of averages for the spectrum. Currently the noise 
-of the curves is about 20 dBpk-pk and it doesn’t allow to appreciate the 
+- Please increase the number of averages for the spectrum. Currently the noise    % r2.16 - fait
+of the curves is about 20 dBpk-pk and it doesn’t allow to appreciate the
 differences among the curves. I suggest to reduce the noise below 1 dBpk-pk.
 }
  
@@ -216,14 +231,13 @@ mais que tu as des jeux de donnees de e.g. 10000 points, on peut faire des moyen
 sur les sequences successives. Au pire si pas possible, une moyenne glissante sur
 chaque spectre pour affiner les traits ?
  
-%In conclusion, my opinion is that the methodology presented in the Manuscript 
-%deserve to be published, provided that the criterion is changed according 
+%In conclusion, my opinion is that the methodology presented in the Manuscript
+%deserve to be published, provided that the criterion is changed according
 %the indications mentioned above.
 \end{document}
 %****************************************************
 %
-%For information about the IEEE Ultrasonics, Ferroelectrics, and Frequency 
-%Control Society, please visit the website: http://www.ieee-uffc.org. The 
-%website of the Transactions on Ultrasonics, Ferroelectrics, and Frequency 
+%For information about the IEEE Ultrasonics, Ferroelectrics, and Frequency
+%Control Society, please visit the website: http://www.ieee-uffc.org. The
+%website of the Transactions on Ultrasonics, Ferroelectrics, and Frequency
 %Control is at: http://ieee-uffc.org/publications/transactions-on-uffc
-
...	...	@@ -24,4 +24,12 @@ ifcs2018_journal.log
24	24	ifcs2018_journal.out
25	25	ifcs2018_journal.pdf
26	26
	27	+ifcs2018_journal_reponse.aux
	28	+ifcs2018_journal_reponse.log
	29	+ifcs2018_journal_reponse.pdf
	30	+
	31	+cover.aux
	32	+cover.log
	33	+cover.pdf
	34	+
27	35	*.bak
...	...	@@ -34,6 +34,10 @@ $(TARGET)_journal: $(TARGET)_journal.tex references.bib biblio.bib
34	34	$(TEX) $@.tex
35	35	$(TEX) $@.tex
36	36
	37	+$(TARGET)_journal_reponse: $(TARGET)_journal_reponse.tex references.bib biblio.bib
	38	+ $(TEX) $@.tex
	39	+ $(TEX) $@.tex
	40	+
37	41	clean:
38	42	rm -f $(TARGET)_abstract.aux $(TARGET)_abstract.log $(TARGET)_abstract.out $(TARGET)_abstract.bbl $(TARGET)_abstract.blg
39	43	rm -f $(TARGET)_poster.aux $(TARGET)_poster.log $(TARGET)_poster.out
...	...	@@ -23,6 +23,8 @@
23	23	\usetikzlibrary{positioning,fit}
24	24	\usepackage{multirow}
25	25	\usepackage{scalefnt}
	26	+\usepackage{caption}
	27	+\usepackage{subcaption}
26	28
27	29	% correct bad hyphenation here
28	30	\hyphenation{op-tical net-works semi-conduc-tor}
...	...	@@ -35,8 +37,8 @@ to oscillator metrology}
35	37
36	38	\author{\IEEEauthorblockN{A. Hugeat\IEEEauthorrefmark{1}\IEEEauthorrefmark{2}, J. Bernard\IEEEauthorrefmark{2},
37	39	G. Goavec-M\'erou\IEEEauthorrefmark{1},
38		-P.-Y. Bourgeois\IEEEauthorrefmark{1}, J.-M. Friedt\IEEEauthorrefmark{1}}
39		-\IEEEauthorblockA{\IEEEauthorrefmark{1}FEMTO-ST, Time \& Frequency department, Besan\c con, France }
	40	+P.-Y. Bourgeois\IEEEauthorrefmark{1}, J.-M. Friedt\IEEEauthorrefmark{1}}\\
	41	+\IEEEauthorblockA{\IEEEauthorrefmark{1}FEMTO-ST, Time \& Frequency department, Besan\c con, France }\\
40	42	\IEEEauthorblockA{\IEEEauthorrefmark{2}FEMTO-ST, Computer Science department DISC, Besan\c con, France \\
41	43	Email: \{pyb2,jmfriedt\}@femto-st.fr}
42	44	}
...	...	@@ -280,17 +282,20 @@ the stopband the last 40\%, allowing 20\% transition width.}
280	282	\end{figure}
281	283
282	284	In the transition band, the behavior of the filter is left free, we only care about the passband and the stopband characteristics.
283		-Our initial criterion considered the mean value of the stopband rejection, as shown in figure~\ref{fig:mean_criterion}. This criterion
284		-yields unacceptable results since notches overestimate the rejection capability of the filter. Furthermore, the losses within
285		-the passband are not considered and might be excessive for excessively wide transitions widths introduced for filters with few coefficients.
286		-Such biases are compensated for by the second considered criterion which is based on computing the maximum rejection within the stopband minus the mean of the absolute value of passband rejection. With this criterion, the results are significantly improved as shown in figure~\ref{fig:custom_criterion} and meet the expected rejection capability of low pass filters.
287		-
288		-\begin{figure}
289		-\centering
290		-\includegraphics[width=\linewidth]{images/colored_mean_criterion}
291		-\caption{Mean stopband rejection criterion comparison between monolithic filter and cascaded filters}
292		-\label{fig:mean_criterion}
293		-\end{figure}
	285	+% r2.7
	286	+% Our initial criterion considered the mean value of the stopband rejection, as shown in figure~\ref{fig:mean_criterion}. This criterion
	287	+% yields unacceptable results since notches overestimate the rejection capability of the filter. Furthermore, the losses within
	288	+% the passband are not considered and might be excessive for excessively wide transitions widths introduced for filters with few coefficients.
	289	+Our criterion to compute the filter rejection takes
	290	+% r2.8 et r2.2 r2.3
	291	+the maximum magnitude within the stopband minus the sum of the absolute value of passband rejection. With this criterion, we meet the expected rejection capability of low pass filters as shown in figure~\ref{fig:custom_criterion}.
	292	+
	293	+% \begin{figure}
	294	+% \centering
	295	+% \includegraphics[width=\linewidth]{images/colored_mean_criterion}
	296	+% \caption{Mean stopband rejection criterion comparison between monolithic filter and cascaded filters}
	297	+% \label{fig:mean_criterion}
	298	+% \end{figure}
294	299
295	300	\begin{figure}
296	301	\centering
...	...	@@ -324,9 +329,11 @@ the previous relation is no longer valid as illustrated on figure~\ref{fig:sum_r
324	329	are two different filters with maximums and notches not located at the same frequency offsets.
325	330	Hence when summing the transfer functions, the resulting rejection shown as the dashed yellow line is improved
326	331	with respect to a basic sum of the rejection criteria shown as a the dotted yellow line.
327		-Thus, estimating the rejection of filter cascades is more complex than takin the sum of all the rejection
	332	+% r2.9
	333	+Thus, estimating the rejection of filter cascades is more complex than taking the sum of all the rejection
328	334	criteria of each filter. However since the this sum underestimates the rejection capability of the cascade,
329		-this upper bound is considered as a pessimistic and acceptable criterion for deciding on the suitability
	335	+% r2.10
	336	+this upper bound is considered as a conservative and acceptable criterion for deciding on the suitability
330	337	of the filter cascade to meet design criteria.
331	338
332	339	\begin{figure}
...	...	@@ -336,8 +343,14 @@ of the filter cascade to meet design criteria.
336	343	\label{fig:sum_rejection}
337	344	\end{figure}
338	345
	346	+% r2.6
	347	+Finally in our case, we consider that the input signal are fully known. So the
	348	+resolution of the data stream are fixed and still the same for all experiments
	349	+in this paper.
	350	+
339	351	Based on this analysis, we address the estimate of resource consumption (called
340		-silicon area -- in the case of FPGAs meaning processing cells) as a function of
	352	+% r2.11
	353	+silicon area -- in the case of FPGAs this means processing cells) as a function of
341	354	filter characteristics. As a reminder, we do not aim at matching actual hardware
342	355	configuration but consider an arbitrary silicon area occupied by each processing function,
343	356	and will assess after synthesis the adequation of this arbitrary unit with actual
...	...	@@ -383,7 +396,12 @@ Finally, equation~\ref{eq:init} gives the number of bits of the global input.
383	396
384	397	This model is non-linear and even non-quadratic, as $F$ does not have a known
385	398	linear or quadratic expression. We introduce $p$ FIR configurations
386		-$(C_{ij}, \pi_{ij}^C), 1 \leq j \leq p$ that are constants. We define binary
	399	+$(C_{ij}, \pi_{ij}^C), 1 \leq j \leq p$ that are constants.
	400	+% r2.12
	401	+This variable must be defined by the user, it represent the number of different
	402	+set of coefficients generated (for memory, we use \texttt{firls} and \texttt{fir1}
	403	+functions from GNU Octave).
	404	+We define binary
387	405	variable $\delta_{ij}$ that has value 1 if stage~$i$ is in configuration~$j$
388	406	and 0 otherwise. The new equations are as follows:
389	407
...	...	@@ -398,7 +416,10 @@ Equations \ref{eq:areadef2}, \ref{eq:rejectiondef2} and \ref{eq:bits2} replace
398	416	respectively equations \ref{eq:areadef}, \ref{eq:rejectiondef} and \ref{eq:bits}.
399	417	Equation~\ref{eq:config} states that for each stage, a single configuration is chosen at most.
400	418
401		-This modified model is quadratic, and it can be linearised if necessary. The Gurobi
	419	+% r2.13
	420	+This modified model is quadratic since we multiply two variables in the
	421	+equation~\ref{eq:areadef2} ($\delta_{ij}$ by $\pi_{ij}^-$) but it can be linearised if necessary.
	422	+The Gurobi
402	423	(\url{www.gurobi.com}) optimization software is used to solve this quadratic
403	424	model, and since Gurobi is able to linearize, the model is left as is. This model
404	425	has $O(np)$ variables and $O(n)$ constraints.
...	...	@@ -602,25 +623,48 @@ Figure~\ref{fig:max_500_result} shows the rejection of the different configurati
602	623	Figure~\ref{fig:max_1000_result} shows the rejection of the different configurations in the case of MAX/1000.
603	624	Figure~\ref{fig:max_1500_result} shows the rejection of the different configurations in the case of MAX/1500.
604	625
	626	+% \begin{figure}
	627	+% \centering
	628	+% \includegraphics[width=\linewidth]{images/max_500}
	629	+% \caption{Signal spectrum for MAX/500}
	630	+% \label{fig:max_500_result}
	631	+% \end{figure}
	632	+%
	633	+% \begin{figure}
	634	+% \centering
	635	+% \includegraphics[width=\linewidth]{images/max_1000}
	636	+% \caption{Signal spectrum for MAX/1000}
	637	+% \label{fig:max_1000_result}
	638	+% \end{figure}
	639	+%
	640	+% \begin{figure}
	641	+% \centering
	642	+% \includegraphics[width=\linewidth]{images/max_1500}
	643	+% \caption{Signal spectrum for MAX/1500}
	644	+% \label{fig:max_1500_result}
	645	+% \end{figure}
	646	+
	647	+% r2.14 et r2.15 et r2.16
605	648	\begin{figure}
606		-\centering
607		-\includegraphics[width=\linewidth]{images/max_500}
608		-\caption{Signal spectrum for MAX/500}
609		-\label{fig:max_500_result}
610		-\end{figure}
611		-
612		-\begin{figure}
613		-\centering
614		-\includegraphics[width=\linewidth]{images/max_1000}
615		-\caption{Signal spectrum for MAX/1000}
616		-\label{fig:max_1000_result}
617		-\end{figure}
618		-
619		-\begin{figure}
620		-\centering
621		-\includegraphics[width=\linewidth]{images/max_1500}
622		-\caption{Signal spectrum for MAX/1500}
623		-\label{fig:max_1500_result}
	649	+ \centering
	650	+ \begin{subfigure}{\linewidth}
	651	+ \includegraphics[width=\linewidth]{images/max_500}
	652	+ \caption{Signal spectrum for MAX/500}
	653	+ \label{fig:max_500_result}
	654	+ \end{subfigure}
	655	+
	656	+ \begin{subfigure}{\linewidth}
	657	+ \includegraphics[width=\linewidth]{images/max_1000}
	658	+ \caption{Signal spectrum for MAX/1000}
	659	+ \label{fig:max_1000_result}
	660	+ \end{subfigure}
	661	+
	662	+ \begin{subfigure}{\linewidth}
	663	+ \includegraphics[width=\linewidth]{images/max_1500}
	664	+ \caption{Signal spectrum for MAX/1500}
	665	+ \label{fig:max_1500_result}
	666	+ \end{subfigure}
	667	+ \caption{Signal spectrum of each experimental configurations MAX/500, MAX/1000 and MAX/1500}
624	668	\end{figure}
625	669
626	670	In all cases, we observe that the actual rejection is close to the rejection computed by the solver.
...	...	@@ -827,32 +871,61 @@ Figure~\ref{fig:min_60} shows the rejection of the different configurations in t
827	871	Figure~\ref{fig:min_80} shows the rejection of the different configurations in the case of MIN/80.
828	872	Figure~\ref{fig:min_100} shows the rejection of the different configurations in the case of MIN/100.
829	873
	874	+% \begin{figure}
	875	+% \centering
	876	+% \includegraphics[width=\linewidth]{images/min_40}
	877	+% \caption{Signal spectrum for MIN/40}
	878	+% \label{fig:min_40}
	879	+% \end{figure}
	880	+%
	881	+% \begin{figure}
	882	+% \centering
	883	+% \includegraphics[width=\linewidth]{images/min_60}
	884	+% \caption{Signal spectrum for MIN/60}
	885	+% \label{fig:min_60}
	886	+% \end{figure}
	887	+%
	888	+% \begin{figure}
	889	+% \centering
	890	+% \includegraphics[width=\linewidth]{images/min_80}
	891	+% \caption{Signal spectrum for MIN/80}
	892	+% \label{fig:min_80}
	893	+% \end{figure}
	894	+%
	895	+% \begin{figure}
	896	+% \centering
	897	+% \includegraphics[width=\linewidth]{images/min_100}
	898	+% \caption{Signal spectrum for MIN/100}
	899	+% \label{fig:min_100}
	900	+% \end{figure}
	901	+
	902	+% r2.14 et r2.15 et r2.16
830	903	\begin{figure}
831		-\centering
832		-\includegraphics[width=\linewidth]{images/min_40}
833		-\caption{Signal spectrum for MIN/40}
834		-\label{fig:min_40}
835		-\end{figure}
836		-
837		-\begin{figure}
838		-\centering
839		-\includegraphics[width=\linewidth]{images/min_60}
840		-\caption{Signal spectrum for MIN/60}
841		-\label{fig:min_60}
842		-\end{figure}
843		-
844		-\begin{figure}
845		-\centering
846		-\includegraphics[width=\linewidth]{images/min_80}
847		-\caption{Signal spectrum for MIN/80}
848		-\label{fig:min_80}
849		-\end{figure}
850		-
851		-\begin{figure}
852		-\centering
853		-\includegraphics[width=\linewidth]{images/min_100}
854		-\caption{Signal spectrum for MIN/100}
855		-\label{fig:min_100}
	904	+ \centering
	905	+ \begin{subfigure}{\linewidth}
	906	+ \includegraphics[width=\linewidth]{images/min_40}
	907	+ \caption{Signal spectrum for MIN/40}
	908	+ \label{fig:min_40}
	909	+ \end{subfigure}
	910	+
	911	+ \begin{subfigure}{\linewidth}
	912	+ \includegraphics[width=\linewidth]{images/min_60}
	913	+ \caption{Signal spectrum for MIN/60}
	914	+ \label{fig:min_60}
	915	+ \end{subfigure}
	916	+
	917	+ \begin{subfigure}{\linewidth}
	918	+ \includegraphics[width=\linewidth]{images/min_80}
	919	+ \caption{Signal spectrum for MIN/80}
	920	+ \label{fig:min_80}
	921	+ \end{subfigure}
	922	+
	923	+ \begin{subfigure}{\linewidth}
	924	+ \includegraphics[width=\linewidth]{images/min_100}
	925	+ \caption{Signal spectrum for MIN/100}
	926	+ \label{fig:min_100}
	927	+ \end{subfigure}
	928	+ \caption{Signal spectrum of each experimental configurations MIN/40, MIN/60, MIN/80 and MIN/100}
856	929	\end{figure}
857	930
858	931	We observe that all rejections given by the quadratic solver are close to the experimentally
1	1	%Minor Revision - TUFFC-09469-2019
2		-%Transactions on Ultrasonics, Ferroelectrics, and Frequency
	2	+%Transactions on Ultrasonics, Ferroelectrics, and Frequency
3	3	%Control (July 23, 2019 9:29 PM)
4		-%To: arthur.hugeat@femto-st.fr, julien.bernard@femto-st.fr,
5		-%gwenhael.goavec@femto-st.fr, pyb2@femto-st.fr, pierre-yves.bourgeois@femto-st.fr,
	4	+%To: arthur.hugeat@femto-st.fr, julien.bernard@femto-st.fr,
	5	+%gwenhael.goavec@femto-st.fr, pyb2@femto-st.fr, pierre-yves.bourgeois@femto-st.fr,
6	6	%jmfriedt@femto-st.fr
7	7	%CC: giorgio.santarelli@institutoptique.fr, lewin@ece.drexel.edu
8	8	%
...	...	@@ -12,56 +12,56 @@
12	12	%
13	13	%MANUSCRIPT NO. TUFFC-09469-2019
14	14	%MANUSCRIPT TYPE: Papers
15		-%TITLE: Filter optimization for real time digital processing of radiofrequency
	15	+%TITLE: Filter optimization for real time digital processing of radiofrequency
16	16	%signals: application to oscillator metrology
17		-%AUTHOR(S): HUGEAT, Arthur; BERNARD, Julien; Goavec-Mérou, Gwenhaël; Bourgeois,
	17	+%AUTHOR(S): HUGEAT, Arthur; BERNARD, Julien; Goavec-Mérou, Gwenhaël; Bourgeois,
18	18	%Pierre-Yves; Friedt, Jean-Michel
19	19	%
20		-%has been reviewed and it has been suggested that it be accepted for publication
21		-%after minor revisions. In your revision, you must respond to the reviewer’s
	20	+%has been reviewed and it has been suggested that it be accepted for publication
	21	+%after minor revisions. In your revision, you must respond to the reviewer’s
22	22	%comments at the end of this e-mail or attached.
23	23	%
24		-%Your revised manuscript must be submitted within the next THREE WEEKS. If you
25		-%are not able to submit your manuscript in this time frame, you must contact the
	24	+%Your revised manuscript must be submitted within the next THREE WEEKS. If you
	25	+%are not able to submit your manuscript in this time frame, you must contact the
26	26	%Editor in Chief (Peter Lewin, lewinpa@drexel.edu).
27	27	%
28		-%Please resubmit your revised manuscript to the Transactions on Ultrasonics,
29		-%Ferroelectrics, and Frequency Control Manuscript Central website at
30		-%http://mc.manuscriptcentral.com/tuffc-ieee. From the “Author Center” select
31		-%“Manuscripts with Decisions” and under the appropriate manuscript ID select
	28	+%Please resubmit your revised manuscript to the Transactions on Ultrasonics,
	29	+%Ferroelectrics, and Frequency Control Manuscript Central website at
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	31	+%“Manuscripts with Decisions” and under the appropriate manuscript ID select
32	32	%“create a revision”.
33	33	%
34	34	%To expedite the review of your resubmission:
35	35	%
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38		-%Failure to address reviewers comments can still lead to a rejection of your
	36	+%(1) Include or attach a point by point response to reviewer’s comments and
	37	+%detail all changes made in your manuscript under “Response to Decision Letter”.
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40		-%(2) Submit a PDF of the revised manuscript using the “Formatted (Double Column)
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59	59	%to us and we will not be able to continue to process your manuscript.
60	60	%
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	62	+%mandatory page charges in the "Guideline for Authors" at
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65	65	%excess of 8 pages.
66	66	%
67	67	%Sincerely,
...	...	@@ -82,22 +82,22 @@
82	82	%In general, the language/grammar is adequate.
83	83
84	84	{\bf
85		-On page 2, "...allowing to save processing resource..." could be improved.
	85	+On page 2, "...allowing to save processing resource..." could be improved. % r1.1
86	86
87		-On page 2, "... or thanks at a radiofrequency-grade..." isn't at all clear what
	87	+On page 2, "... or thanks at a radiofrequency-grade..." isn't at all clear what % r1.2
88	88	the author meant.
89	89
90		-One page 2, the whole paragraph "The first step of our approach is to model..."
	90	+One page 2, the whole paragraph "The first step of our approach is to model..." % r1.3
91	91	could be improved.
92	92	}
93	93
94	94	{\bf
95		-I appreciate that the authors attempted and document two optimizations: that
96		-of maximum rejection ratio at fixed silicon area, as well as minimum silicon
97		-area for a fixed minimum rejection ratio. For non-experts, it might be very
98		-useful to compare the results of both optimization paths to the performance and
99		-resource-utilization of generic low-pass filter gateware offered by device
100		-manufacturers. I appreciate also that the authors have presented source code
	95	+I appreciate that the authors attempted and document two optimizations: that % r1.4 - en attente des résultats
	96	+of maximum rejection ratio at fixed silicon area, as well as minimum silicon
	97	+area for a fixed minimum rejection ratio. For non-experts, it might be very
	98	+useful to compare the results of both optimization paths to the performance and
	99	+resource-utilization of generic low-pass filter gateware offered by device
	100	+manufacturers. I appreciate also that the authors have presented source code
101	101	for examination online.
102	102	}
103	103
...	...	@@ -109,34 +109,34 @@ Reviewer: 2
109	109	}
110	110
111	111	%Comments to the Author
112		-%In the Manuscript, the Authors describe an optimization methodology for filter
113		-%design to be used in phase noise metrology. The methodology is general and can
114		-%be used for many aspects of the processing chain. In the Manuscript, the Authors
115		-%focus on filtering and shifting while the other aspects, in particular decimation,
116		-%will be considered in a future work. The optimization problem is modelled
117		-%theoretically and then solved by means of a commercial software. The solutions
118		-%are tested experimentally on the Redpitaya platform with synthetic and real
119		-%white noises. Two cases are considered as a function of the number of filters:
120		-%maximum rejection given a fixed amount of resources and minimum resource
121		-%utilization given a fixed amount of rejection.
122		-%The Authors find that filtering improves significantly when the number of
123		-%filters increases.
124		-%A lot of work has been done in generalizing and automating the procedure so
125		-%that different approaches can be investigated quickly and efficiently. The
126		-%results presented in the Manuscript seem to be just a case study based on
127		-%the particular criterion chosen by the Authors. Different criteria, in
128		-%general, could lead to different results and it is important to consider
129		-%carefully the criterion adopted by the Authors, in order to check if it
130		-%is adequate to compare the performance of filters and if multi-stage
	112	+%In the Manuscript, the Authors describe an optimization methodology for filter
	113	+%design to be used in phase noise metrology. The methodology is general and can
	114	+%be used for many aspects of the processing chain. In the Manuscript, the Authors
	115	+%focus on filtering and shifting while the other aspects, in particular decimation,
	116	+%will be considered in a future work. The optimization problem is modelled
	117	+%theoretically and then solved by means of a commercial software. The solutions
	118	+%are tested experimentally on the Redpitaya platform with synthetic and real
	119	+%white noises. Two cases are considered as a function of the number of filters:
	120	+%maximum rejection given a fixed amount of resources and minimum resource
	121	+%utilization given a fixed amount of rejection.
	122	+%The Authors find that filtering improves significantly when the number of
	123	+%filters increases.
	124	+%A lot of work has been done in generalizing and automating the procedure so
	125	+%that different approaches can be investigated quickly and efficiently. The
	126	+%results presented in the Manuscript seem to be just a case study based on
	127	+%the particular criterion chosen by the Authors. Different criteria, in
	128	+%general, could lead to different results and it is important to consider
	129	+%carefully the criterion adopted by the Authors, in order to check if it
	130	+%is adequate to compare the performance of filters and if multi-stage
131	131	%filters are really superior than monolithic filters.
132	132
133	133	{\bf
134		-By observing the results presented in fig. 10-16, it is clear that the
135		-performances of multi-stage filters are obtained at the expense of their
136		-selectivity and, in this sense, the filters presented in these figures
137		-are not equivalent. For example, in Fig. 14, at the limit of the pass band,
138		-the attenuation is almost 15 dB for n = 5, while it is not noticeable for
139		-n = 1.
	134	+By observing the results presented in fig. 10-16, it is clear that the % r2.1 - fait
	135	+performances of multi-stage filters are obtained at the expense of their
	136	+selectivity and, in this sense, the filters presented in these figures
	137	+are not equivalent. For example, in Fig. 14, at the limit of the pass band,
	138	+the attenuation is almost 15 dB for n = 5, while it is not noticeable for
	139	+n = 1.
140	140	}
141	141
142	142	TODO : ajouter les gabarits
...	...	@@ -145,14 +145,16 @@ Peut etre refaire une serie de simulation dans lesquelles on impose une coupure
145	145	non pas entre 40 et 60\% mais entre 50 et 60\% pour demontrer que l'outil s'adapte
146	146	au critere qu'on lui impose, et que la coupure moins raide n'est pas intrinseque
147	147	a la cascade de filtres.
	148	+AH: Je finis les corrections, je poste l'article revu et pendant ce temps j'essaie de
	149	+relancer des expérimentations. Si j'arrive à les finir à temps, je les intégrerai
148	150
149	151	{\bf
150		-The reason is in the criterion that considers the average attenuation in
151		-the pass band. This criterion does not take into account the maximum attenuation
152		-in this region, which is a very important parameter for specifying a filter
153		-and for evaluating its performance. For example, with this criterion, a
154		-filter with 0.1 dB of ripple is considered equivalent to a filter with
155		-10 dB of ripple. This point has a strong impact in the optimization process
	152	+The reason is in the criterion that considers the average attenuation in % r2.2 - fait
	153	+the pass band. This criterion does not take into account the maximum attenuation
	154	+in this region, which is a very important parameter for specifying a filter
	155	+and for evaluating its performance. For example, with this criterion, a
	156	+filter with 0.1 dB of ripple is considered equivalent to a filter with
	157	+10 dB of ripple. This point has a strong impact in the optimization process
156	158	and in the results that are obtained and has to be reconsidered.
157	159	}
158	160
...	...	@@ -160,54 +162,67 @@ Je ne pense pas que ca soit le cas : la somme des valeurs absolues des pertes
160	162	dans la bande va defavoriser un filtre avec 10 dB de ripples. Il n'a pas compris que
161	163	la bandpass s'arrete a 40\% de la bande, donc mettre le gabarit clarifierait ce point je
162	164	pense
	165	+AH: Il y avait une faute, j'avais mis "mean of absolute value" au lieu de "sum of absolute value". Je pense que je n'ai pas besoin de mettre plus de détail ?
163	166
164	167	{\bf
165		-I strongly suggest to re-run the analysis with a criterion that takes also
166		-into account the maximum allowed attenuation in pass band, for example by
167		-fixing its value to a typical one, as it has been done for the transition
168		-bandwidth.
	168	+I strongly suggest to re-run the analysis with a criterion that takes also % r2.3 -fait
	169	+into account the maximum allowed attenuation in pass band, for example by
	170	+fixing its value to a typical one, as it has been done for the transition
	171	+bandwidth.
169	172	}
	173	+AH: Il y avait une faute, j'avais mis "mean of absolute value" au lieu de "sum of absolute value". Je pense que je n'ai pas besoin de mettre plus de détail ?
170	174
171	175	{\bf
172		-In addition, I suggest to address the following points:
173		-- Page 1, line 50: the Authors state that IIR have shorter impulse response
	176	+In addition, I suggest to address the following points: % r2.4
	177	+- Page 1, line 50: the Authors state that IIR have shorter impulse response
174	178	than FIR. This is not true in general. The sentence should be reconsidered.
175	179	}
176	180
177	181	J'aurais du dire ``lag'' au lieu de ``impulse response'' je pense
	182	+AH: Je ne comprends pas trop ce qui ne va pas ici
178	183
179	184	{\bf
180		-- Fig. 4: the Author should motivate in the text why it has been chosen
181		-this transition bandwidth and if it is a typical requirement for phase-noise
	185	+- Fig. 4: the Author should motivate in the text why it has been chosen % r2.5
	186	+this transition bandwidth and if it is a typical requirement for phase-noise
182	187	metrology.
183		-- The impact of the coefficient resolution is discussed. What about the
184		-resolution of the data stream? Is it fixed? If so, which value has been
185		-used in the analysis? If not, how is it changed with respect to the
	188	+}
	189	+AH: Je ne sais pas comment justifier ça. Je dois dire que comme ça on peut éventuellement
	190	+décimer par deux le flux ?
	191	+
	192	+{\bf
	193	+- The impact of the coefficient resolution is discussed. What about the % r2.6 - fait
	194	+resolution of the data stream? Is it fixed? If so, which value has been
	195	+used in the analysis? If not, how is it changed with respect to the
186	196	coefficient resolution?
187	197	}
188	198
189	199	Pr\'eciser que le flux de donn\'ees en entr\'ees est de r\'esolution fixe
190	200
191	201	{\bf
192		-- Page 3, line 47: the initial criterion can be omitted and, consequently,
	202	+- Page 3, line 47: the initial criterion can be omitted and, consequently, % r2.7 - fait
193	203	Fig. 5 can be removed.
194		-- Page 3, line 55: “maximum rejection” is not compatible with fig. 4.
	204	+- Page 3, line 55: “maximum rejection” is not compatible with fig. 4. % r2.8 - fait
195	205	It should be “minimum”
196		-- Page e, line 55, second column: “takin”
197		-- Page 3, line 58: “pessimistic” should be replaced with “conservative”
198		-- Page 4, line 17: “meaning” --> “this means”
199		-- Page 4, line 10: how $p$ is chosen? Which is the criterion used to choose
	206	+}
	207	+AH: Je ne suis pas d'accord, le critère n'est pas le min de la rejection mais le max
	208	+de la magnitude. J'ai corrigé en ce sens.
	209	+
	210	+{\bf
	211	+- Page e, line 55, second column: “takin” % r2.9 - fait
	212	+- Page 3, line 58: “pessimistic” should be replaced with “conservative” % r2.10 - fait
	213	+- Page 4, line 17: “meaning” --> “this means” % r2.11 - fait
	214	+- Page 4, line 10: how $p$ is chosen? Which is the criterion used to choose % r2.12 - fait
200	215	these particular configurations? Are they chosen automatically?
201		-- Page 4, line 31: how does the delta function transform model from non-linear
	216	+- Page 4, line 31: how does the delta function transform model from non-linear % r2.13 - fait
202	217	and non-quadratic to a quadratic?
203		-- Captions of figure and tables are too minimal.
204		-- Figures can be grouped: fig. 10-12 can be grouped as three subplots (a, b, c)
205		-of a single figure. Same for fig. 13-16.
	218	+- Captions of figure and tables are too minimal. % r2.14
	219	+- Figures can be grouped: fig. 10-12 can be grouped as three subplots (a, b, c) % r2.15 - fait
	220	+of a single figure. Same for fig. 13-16.
206	221	}
207	222
208	223	{\bf
209		-- Please increase the number of averages for the spectrum. Currently the noise
210		-of the curves is about 20 dBpk-pk and it doesn’t allow to appreciate the
	224	+- Please increase the number of averages for the spectrum. Currently the noise % r2.16 - fait
	225	+of the curves is about 20 dBpk-pk and it doesn’t allow to appreciate the
211	226	differences among the curves. I suggest to reduce the noise below 1 dBpk-pk.
212	227	}
213	228
...	...	@@ -216,14 +231,13 @@ mais que tu as des jeux de donnees de e.g. 10000 points, on peut faire des moyen
216	231	sur les sequences successives. Au pire si pas possible, une moyenne glissante sur
217	232	chaque spectre pour affiner les traits ?
218	233
219		-%In conclusion, my opinion is that the methodology presented in the Manuscript
220		-%deserve to be published, provided that the criterion is changed according
	234	+%In conclusion, my opinion is that the methodology presented in the Manuscript
	235	+%deserve to be published, provided that the criterion is changed according
221	236	%the indications mentioned above.
222	237	\end{document}
223	238	%****************************************************
224	239	%
225		-%For information about the IEEE Ultrasonics, Ferroelectrics, and Frequency
226		-%Control Society, please visit the website: http://www.ieee-uffc.org. The
227		-%website of the Transactions on Ultrasonics, Ferroelectrics, and Frequency
	240	+%For information about the IEEE Ultrasonics, Ferroelectrics, and Frequency
	241	+%Control Society, please visit the website: http://www.ieee-uffc.org. The
	242	+%website of the Transactions on Ultrasonics, Ferroelectrics, and Frequency
228	243	%Control is at: http://ieee-uffc.org/publications/transactions-on-uffc
229		-