%Minor Revision - TUFFC-09469-2019
%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,
%jmfriedt@femto-st.fr
%CC: giorgio.santarelli@institutoptique.fr, lewin@ece.drexel.edu
%
%Dear Mr. Arthur HUGEAT
%
%Congratulations! Your manuscript
%
%MANUSCRIPT NO. TUFFC-09469-2019
%MANUSCRIPT TYPE: Papers
%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,
%Pierre-Yves; Friedt, Jean-Michel
%
%has been reviewed and it has been suggested that it be accepted for publication
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%****************************************************
%REVIEWERS' COMMENTS:

\documentclass[a4paper]{article}
\usepackage{fullpage,graphicx}
\begin{document}
{\bf Reviewer: 1}

%Comments to the Author
%In general, the language/grammar is adequate.

{\bf
On page 2,  "...allowing to save processing resource..." could be improved.       % r1.1
}

The sentence was split and now reads ``number of coefficients irrelevant: processing 
resources are hence saved by shrinking the filter length.''

{\bf
On page 2, "... or thanks at a radiofrequency-grade..." isn't at all clear what   % r1.2
the author meant.}

Grammatical error: this sentence now reads ``or by sampling a wideband (125~MS/s)
Analog to Digital Converter (ADC) loaded by a 50~$\Omega$ resistor.''

{\bf 
On page 2, the whole paragraph "The first step of our approach is to model..."   % r1.3
could be improved.
}

Indeed this paragraph has be written again and now reads as\\
``The first step of our approach is to model the DSP chain. Since we aim at only optimizing
the filtering part of the signal processing chain, we have not included the PRN generator or the
ADC in the model: the input data size and rate are considered fixed and defined by the hardware. 
The filtering can be done in two ways, either by considering a single monolithic FIR filter
requiring many coefficients to reach the targeted noise rejection ratio, or by
cascading multiple FIR filters, each with fewer coefficients than found in the monolithic filter.
''

{\bf
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.
}

TODO : FIR Compiler et regarder les ressources pour un FIR comparable a ceux monolithiques
fournis dans l'article (memes coefs et meme nombre de coefs)

{\bf
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
%filters are really superior than monolithic filters.

{\bf
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

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          % 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.
}

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        % 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:                           % 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.
}

We have not stated that the IIR has a shorter impulse response but a shorter lag.
Indeed while a typical FIR filter will have 32 to 128~coefficients, few IIR filters
have more than 5~coefficients. Hence, while a FIR requires 128 inputs before providing
the first output, an IIR will start providing outputs only 5 time steps after the initial
input starts feeding the IIR. Hence, the issue we address here is lag and not impulse
response. We aimed at making this sentence clearer by stating that ``Since latency is not an issue 
in a openloop phase noise characterization instrument, the large
numbre of taps in the FIR, as opposed to the shorter Infinite Impulse Response (IIR) filter,
is not considered as an issue as would be in a closed loop system in which lag aims at being
minimized to avoid oscillation conditions.
''

{\bf
- 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 purpose of the paper is to demonstrate how a given filter shape can be achieved by
minimizing varous resource criteria. Indeed the stopband and bandpass boundaries can
be questioned: we have selected this filter shape as a typical anti-aliasing filter considering
the the dataflow is to be halved. Hence, selecting a cutoff frequency of 40\% the initial
Nyquist frequency prevents noise from reaching baseband after decimating the dataflow by a
factor of 2. Such ideas are now stated explicitly in the text as ``Throughout this demonstration,
we arbitrarily set a bandpass of 40\% of the Nyquist frequency and a bandstop from 60\%
of the Nyquist frequency to the end of the band, as would be typically selected to prevent
aliasing before decimating the dataflow by 2. The method is however generalized to any filter
shape as long as it is defined from the initial modelling steps: Fig. \ref{fig:rejection_pyramid}
as described below is indeed unique for each filter shape.''

{\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?
}

We have now stated in the beginning of the document that ``we have not included the PRN generator 
or the ADC in the model: the input data size and rate are considered fixed and defined by the 
hardware.'' so indeed the input datastream resolution is considered as a given.

{\bf
- 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.             % r2.8  - fait
It should be ``minimum''
}
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    % r2.13 - fait
and non-quadratic to a quadratic?}

JMF : il faudra mettre une phrase qui explique, ca en lisant cette reponse dans l'article
je ne comprends pas comment ca repond a la question

{\bf
- 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    % 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.
}

Indeed averaging had been omitted during post-processing and figure generation: we 
are grateful to the reviewer for emphasizing this point which has now been corrected. All spectra
now exhibit sub-dBpk-pl line thickness.

%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}
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