Jean-Adrien Vernhes
email: jean-adrien.vernhes@tesa.prd.fr

Marie Chabert
email: marie.chabert@enseeiht.fr

Bernard Lacaze

Guy Lesthievent
email: guy.lesthievent@cnes.fr

Roland Baudin
email: roland.baudin@thalesaleniaspace.com

Marie-Laure Boucheret

Adaptive Estimation and Compensation of the Time Delay in a Periodic Non-uniform Sampling Scheme

High sampling rate Analog-to-Digital Converters (ADCs) can be obtained by time-interleaving low rate (and thus low cost) ADCs into so-called Time-Interleaved ADCs (TI-ADCs). Nevertheless increasing the sampling frequency involves an increasing sensibility of the system to desynchronization between the different ADCs that leads to time-skew errors, impacting the system with non linear distortions. The estimation and compensation of these errors are considered as one of the main challenge to deal with in TI-ADCs. Some methods have been previously proposed, mainly in the field of circuits and systems, to estimate the time-skew error but they mainly involve hardware correction and they lack of flexibility, using an inflexible uniform sampling reference. In this paper, we propose to model the output of L interleaved and desynchronized ADCs with a sampling scheme called Periodic Non-uniform Sampling of order L (PNSL). This scheme has been initially proposed as an alternative to uniform sampling for aliasing cancellation, particularly in the case of bandpass signals. We use its properties here to develop a flexible on-line digital estimation and compensation method of the time delays between the desynchronized channels. The estimated delay is exploited in the PNSL reconstruction formula leading to an accurate reconstruction without hardware correction and without any need to adapt the sampling operation. Our method can be used in a simple Built-In Self-Test (BIST) strategy with the use of learning sequences and our model appears more flexible and less electronically expensive, following the principles of "Dirty Radio Frequency" paradigm: designing imperfect analog circuits with subsequently digital corrections of these imperfections.

I. INTRODUCTION

In many areas such as satellite communications, the transmitted signals are characterized by very high frequencies, sometimes beyond the GHz order. In this case, the conversion of an analog signal into a digital one, performed by Analog-to-Digital Converters (ADCs), becomes a challenging operation related to the frequency sampling it requires [START_REF] Murmann | A/D converter trends: Power dissipation, scaling and digitally assisted architectures[END_REF]. In particular applications, because of economical and technological constraints, alternative solutions have to be considered. The most popular one rely on Time Interleaved ADCs (TI-ADCs) [START_REF] Black | Time interleaved converter arrays[END_REF], [START_REF] Khoini-Poorfard | Time-interleaved oversampling convertors[END_REF]. TI-ADCs are composed of several ADC operating at the same sampling frequency f s which are time interleaved in order to reach a higher global sampling frequency by sharing the sampling operation between the different components, at the prize of a strong synchronization between them. Indeed, TI-ADCs are particularly sensitive to desynchronization between the elementary ADCs. The different sampling channels have to be perfectly synchronized to perform the expected uniform sampling operation and limit the effect of time-skew errors as investigated in [START_REF] Elbornsson | Analysis, estimation and compensation of mismatch effects in A/D converters[END_REF], [START_REF] Razavi | Design considerations for interleaved ADCs[END_REF]. Some methods have already been investigated for the desynchronization correction [START_REF] Elbornsson | Blind equalization of time errors in a time-interleaved ADC system[END_REF]- [START_REF] Dogaru | LMS-based RF BIST architecture for multistandard transmitters[END_REF]. Most of these methods propose to further re-synchronize the ADCs for reconstruction error reduction. This implies a lack of flexibility through hardware corrections of the sampling devices and generally an increase in the system complexity and power consumption [START_REF] Razavi | Design considerations for interleaved ADCs[END_REF].

The method proposed in this paper directly operates on the digital signal and does not require any hardware correction. The delay between the ADCs due to desynchronization is first estimated on-line using an adaptive method and then taken into account by non-uniform sampling formulas that perform the signal reconstruction. We developped a simple method suitable for Built-In Self-Test (BIST) [START_REF] Mccluskey | Built-in self-test techniques[END_REF] strategies using learning sequences to calibrate the channels. These sequences can be injected at the input of our system by an auto-calibration method. We follow the principles of "Dirty Radio Frequency" as introduced in [START_REF] Fettweis | Dirty RF: a new paradigm[END_REF], adapting to the desynchronization instead of cancelling it. Nevertheless our method relies on an appropriate model of this desynchronization.

In the case of a TI-ADC composed of L ADCs, we propose to model the system using Periodic Non-uniform Sampling of order L (PNSL), a well-known sampling scheme. In this paper, the derivations are performed for two channels using the so-called PNS2 scheme, previously investigated for its anti-aliasing properties [START_REF] Kohlenberg | Exact interpolation of band-limited functions[END_REF]- [START_REF] Higgins | Some gap sampling series for multiband signals[END_REF] or its efficiency for bandpass signals [START_REF] Lin | Periodically nonuniform sampling of bandpass signals[END_REF], [START_REF] Johansson | Reconstruction of nonuniformly sampled bandlimited signals by means of digital fractional delay filters[END_REF].. The results can be easily extended to the case of L ADCs.For example a TI-ADC with L ADCs denoted ADC 0,...,L-1 can be calibrated by choosing ADC 0 as a reference line and then estimating successively the delay between each ADC 1,...,L-1 and ADC 0 in a PNS2 simple scheme and without lack of generality.

The paper is organized as follows. Section 2 presents the signal and sampling models. Section 3 details the proposed method. The performance analysis is conducted in section 4. Section 5 contains the concluding remarks.

II. SIGNAL MODEL AND SAMPLING SCHEME

A. Signal model and folded spectrum definition

For generality and possible application to telecommunications, the signal is modeled as a stationary random process X = {X(t), t ∈ R} with zero mean, finite variance and power spectral density s X (f ) defined by:

E[X(t)X * (t -τ )] = ∞ -∞ e 2iπf τ s X (f ) df = K X (τ ) (1)
where E[•] stands for the mathematical expectation and the superscript * for the complex conjugate. Let define the folded spectrum of X as follows. Consider the sampling sequence X λ = {X(n + λ), n ∈ Z} for a normalized sampling rate and λ ∈ [0, 1[. X λ is a zero mean stationary random sequence with spectral density S λ X (f ) defined for f ∈ (-1 2 , 1 2 ) by:

S λ X (f ) = n∈Z s X (f + n)e 2iπnλ . (2)
S λ X (f ) is called the generalized folded spectrum of s X (f ), the spectral density of X. Note that for λ = 0, we have a simple expression of the folded spectrum:

S 0 X (f ) = n∈Z s X (f + n) (3)

B. The PNS2 sampling scheme

The PNSL is a sampling scheme composed of L sequences X a l , l = 1, 2, ..., L. When the sum in (2) contains at most L non-zero terms for each frequency f , an errorless reconstruction of X(t) can be performed under light conditions on delay parameters a l . The case of PNS2 is of particular interest for real bandpass signals whose band is composed of two symmetric intervals of unit length. In the following, we will focus on PNS2 for potential application to telecommunication bandpass signals and the signal power spectrum s X (f ) support is then included in the k th Nyquist band ∆ k defined by:

∆ k = -(k + 1 2 ), -(k - 1 2 ) ∪ k - 1 2 , k + 1 2 (4)
In the case of PNS2, the sampling times are distributed according to two time interleaved periodic sequences {n, n ∈ Z} and {n + a, n ∈ Z} with a ∈ [0, 1[. The resulting mean sampling rate equals 2 and thus fits the signal effective bandwidth. This sampling condition was developed by Landau [START_REF] Landau | Sampling, data transmission, and the Nyquist rate[END_REF] and stipulates that a non-baseband signal with an effective bandwidth of B can be sampled at a rate of 2B and an errorless reconstruction can be performed.

Signal samples are then composed of the two sequences X λ = {X(n + λ), n ∈ Z} with λ = {0, a}. The parameter a controls the delay between the two interleaved uniform sequences. Under the additional condition that 2ka / ∈ Z, the exact reconstruction from an infinite number of samples is derived using the following formula [START_REF] Lacaze | Equivalent circuits for the PNS2 sampling scheme[END_REF]:

       X(t) = A 0 (t) sin [2πk(a -t)] + A a (t) sin [2πkt] sin [2πka] , with: A λ (t) = n∈Z sin [π(t -n -λ)] π(t -n -λ) X(n + λ). (5)
Note that in previous works, the authors have also proposed errorless reconstruction formulas (in terms of meansquared error), whose convergence rate can be increased by the introduction of appropriate filters [START_REF]Filtering from PNS2 sampling[END_REF], [START_REF] Chabert | Fast convergence reconstruction formulas for periodic nonuniform sampling of order 2[END_REF] and which can perform joint reconstruction and interference cancelation or direct analytical signal reconstruction [START_REF] Vernhes | Conversion numériqueanalogique sélective d'un signal passe-bande soumis à des interférences[END_REF], [START_REF] Vernhes | Selective analytic signal construction from a non-uniformly sampled bandpass signal[END_REF].

C. Problem formulation

PNS2 reconstruction formulas (in our case Eq. 5) have been derived under the hypothesis that the time delay a is a priori known. However, in practical applications, this parameter may vary across time because of changes in the physical (mainly thermal) constraints imposed to the TI-ADC. The online estimation of this parameter is thus of particular interest to maintain reconstruction accuracy while avoiding expensive calibration as developed in [START_REF] Dyer | An analog background calibration technique for time-interleaved analog-to-digital converters[END_REF], [START_REF] Rudberg | Calibration of mismatch errors in time interleaved ADCs[END_REF].Moreover, a direct use of this estimate in the reconstruction formulas prevent from the also expensive hardware delay corrections.

The influence of appropriate synchronization and then the impact of time-skew errors has been investigated in [START_REF] Elbornsson | Analysis, estimation and compensation of mismatch effects in A/D converters[END_REF], [START_REF] Razavi | Design considerations for interleaved ADCs[END_REF], [START_REF] Vaughan | The theory of bandpass sampling[END_REF]. In [START_REF] Vaughan | The theory of bandpass sampling[END_REF] the authors showed the challenge of using high frequencies in the transmission of bandpass signals because of the impact on synchronization:

∆ f = πB 2f c B + 1 ∆ t (6)
Indeed the sampling accuracy (the time error in other words, denoted as ∆ t ) becomes increasingly important when the center frequency f c of the signal increases for given bandwidth B and reconstruction precision ∆ f . For example, considering a signal around f c = 230 MHz with a bandwidth B = 50 MHz and a reconstruction precision ∆ f = 1%, we must have a time error ∆ t ≤ 6ps, pushing the sampling time to be known very accurately using reliable methods.

Next section presents an adaptive strategy for the estimation of a from the observation of the sequences X 0 and X a . The algorithm involves a learning sequence to estimate a in an auto-calibration purpose.

III. PROPOSED METHOD: ADAPTIVE ESTIMATION OF THE PNS2 TIME DELAY

A. Method description

This section presents the strategy for the estimation of the time delay between the two channels of a PNS2 sampling scheme. This adaptive strategy is based on the use of a learning sequence, a signal with a priori known spectrum which could be transmitted when the signal of interest shuts down or before a transmission to calibrate the system. This simple methods can be embedded into a Self-Test strategy that does not require further complexity, only few components that are able to create and inject the learning sequence at the input of our system.

Moreover, although the PNS2 sampling scheme deals with bandpass signals as detailed below, the learning sequence is set as a baseband signal, allowing to take advantage of the sampling rate used in our reconstruction system. Indeed, we keep a normalized sampling frequency in each channel of the PNS2 scheme, using the same sequences detailed below. Then, two main approaches can be considered. Our method gives a perfect estimation of a without iteration under the condition that the learning spectrum is known or can be estimated. For that purpose, simulations have been made with the example of a cosine wave. Then, another approach has been studied using a bandlimited white noise. By approximating the spectrum in the calculation, a recursive algorithm helps to estimate a with a very few iterations and simple operations. The simulation results will be detailed in the next section.

B. Principle

First, let consider a linear invariant filter of complex gain µ a (f ). We note µ a [X 0 ] the stationary sequence representing the filtered version of X 0 by µ a (f ) and defined by the correspondence:

µ a (f ) = k α k e -2iπkf ⇐⇒ µ a [X 0 ](n) = k α k X(n -k) (7)
We then define the complex gain of µ a (f ) using generalized folded spectrum (2):

µ a (f ) = S a X (f ) S 0 X (f ) e 2iπf a , f ∈ (- 1 2 , 1 2 ) (8)
and we set by periodicity µ a (f ) = µ a (f + n), n ∈ Z. Now let us form the random sequence D = {D n , n ∈ Z}:

D n = X(n + a) -µ a [X 0 ](n) (9)
It is easy to show that D is orthogonal to X 0 , resulting in the following equality:

E[D n X * (m)] = 0 , ∀(n, m) ∈ Z E[(X(n + a) -µ a [X 0 ](n))X * (m)] = 0 (10)
This serie of equations represents the behaviour when a is known in our system. Now, let introduce the time-skew error that happen in the system by changing the parameter delay from a to an unknown b ∈ [0, 1[ such as b = a. The parameter value a will only remain when we refer to the sampling sequence X a which represents the samples taken according to a. Other occurences of a in the equations above will now be replace by b.

We introduce the following criterion:

σ 2 b = E |X(n + a) -µ b [X 0 ](n)| 2 (11)
which can also be expressed as followed using (1):

σ 2 b = ∞ -∞ e 2iπf a -µ b (f ) 2 s X (f ) df. ( 12
)
It is interesting to note that this criterion is minimum for b = a.

As explained in section III-A the learning remains in baseband and then we have s X (f ) = 0 for f / ∈ (-1 2 , 1 2 ) leading to µ b (f ) = e 2iπf b . In this case, the equation ( 12) reduces to:

σ 2 b = 1 2 -1 2 e 2iπf (b-a) -1 2 s X (f ) df. (13)
In parallel, as µ b (f ) = e 2iπf b the filter reduces to a simple delay filter leading to:

µ b [X 0 ](n) = X(n + b) (14)
and then:

σ 2 b = E |X(n + a) -X(n + b)| 2 (15)
From now on, σ 2 b can be estimated using [START_REF] Yen | On nonuniform sampling of bandwidth-limited signals[END_REF] and the classical Shannon sampling formula for X(n + b) derivation:

µ b [X 0 ](n) = X(n + b) = k sin[π(b -k)] π(b -k) X(n + k) (16)
It is well-known that the series involved in Shannon formula suffers from a poor convergence rate. This rate can be improved in the case of oversampling, following previous results [START_REF] Chabert | Fast convergence reconstruction formulas for periodic nonuniform sampling of order 2[END_REF]. For example, if s

X (f ) = 0 , f / ∈ (-1 2 + ε, 1 2 -ε) and 0 < ε < 1
2 then the reconstruction can be performed with higher convergence rate (in 1 k 2 rather than 1 k ) as follows:

µ b [X 0 ](n) = X(n + b) = k a k X(n + k) a k = 2 (b -k) 2 sin ε 2 (b -k) sin (π - ε 2 )(b -k) . (17)
Putting ( 15) into ( 13) gives an estimation method for a, under the assumption that s X (f ) is a priori known for a given learning sequence. We detail now two examples of learning sequences that leads to simple estimation methods.

C. Examples

As explained previously, σ 2

b can be derived according to Eq. ( 13) for a given learning sequence with known power spectral density s X (f ). In the following, we provide simple closed form expressions of the criterion as functions of parameter a for two particular learning sequences.

1) Cosine wave: For a learning sequence defined as a cosine wave at the frequency f 0 , we have the following spectrum:

s X (f ) = 1 2 (δ(f -f 0 )+δ(f +f 0 )) , -1 2 < f 0 < 1 2 .
Then, from Eq. ( 13):

σ 2 b = 4 sin 2 [πf 0 (b -a)] (18)
Because b is given as a parameter and σ 2 b is estimated through [START_REF] Yen | On nonuniform sampling of bandwidth-limited signals[END_REF] given an estimation that we denote σ 2 b , Eq. ( 18) leads to a straightforward estimation of parameter a as follows:

â = b - 1 2πf 0 arccos 1 - σ 2 b 2 . ( 19
)
2) Bandlimited white noise: This case is a bit different. Indeed, whereas the exact spectrum can be estimated and computed directly through the use of Eq. ( 13), it appears very simple to consider the hypothesis that s X (f ) = 1 on (-

1 2 + ε, 1 2 -ε) , 0 < ε < 1 2
, which is true in mean, and s X (f ) = 0 elsewhere. Under this hypothesis, the criterion can be written as:

σ 2 b ≈ 1 2 -ε -1 2 +ε e 2iπf (b-a) -1 2 df ≈ 2(1 -2ε) (1 -sinc[π(b -a)(1 -2ε)]) (20)
with the convention sinc(x) = sin x x . Using (15) it leads to:

sinc[π(b -a)(1 -2ε)] = 1 - σ 2 b 2(1 -2ε) (21)
that can be resolved using a calculation table of the cardinal sine function

f (x) = sinc[πx(1 -2ε)].
An approximation error will be introduced by considering this hypothesis. Nevertheless, a simple recursive algorithm that iterates the estimation helps to estimate a. As shown by Fig. 2, a few number of iterations are sufficient to estimate a with a satisfying precision. Then with a reasonable number of iterations, an estimation error below 10 -5 is possible whatever the initial error on a.

Algorithm 1: Iterative Algorithm

Initialization:

Set â0 = b.
Choose a threshold K.

Step n:

Set b n = ân-1 .
Estimate σ 2 bn using [START_REF] Yen | On nonuniform sampling of bandwidth-limited signals[END_REF]. Use [START_REF]Filtering from PNS2 sampling[END_REF] and the calculation table to estimate b n -ân .

Until |â n -ân-1 | < K IV. PERFORMANCE ANALYSIS
The simulation results are displayed on Fig. 1 and2. In each case, reconstruction of the signal is performed using sliding windows of length N samp . This parameter will be of interest in the case of the white noise iteration method.

First, Fig. 1 shows the performance of the cosinus estimation, helping to correct the reconstruction errors whatever the initial value of b. This estimation is done using N samp = 10 in a one-tap algorithm without iteration, leading to a very low reconstruction error. It is important to note that the same conditions were used for the blue and red curves, the only difference being the use of cosine estimation on the red curve.

Concerning Fig. 2, the simulations were made choosing the Nyquist band number as k = 3 with ε = 5 100 (5% of the bandwidth). The performance is shown through the plot of the 2 first iterations for each point and then the final estimation result. It is important to note that the dashed line represents the identity line, to which all the points belong initially. Fig. 2 then shows the performance of the estimation of a, at the first iteration, at the second iteration and then the final result, estimated after a certain number of iterations. In the case of N samp = 100 in Fig. 2b, this final result estimated after an average of 20 iterations shows a precision below 10 -5 for almost all the points. Fig. 2a has been tested using the same parameters, except that the reconstruction is now performed with a sliding window of only N samp = 10 samples of the learning sequence. Even with this very low number of data, the estimation is performed quite well and leads to an estimation with a precision of almost 10 -6 for all the points. The number of iterations however increases a bit but it must be related

V. CONCLUSION AND FUTURE WORKS

This article presents a method for the estimation and compensation of unknown delay between the channels in a PNS2 sampling scheme, used to model desynchronization errors in TI-ADCs. The extended case of PNSL that models a L channels TI-ADC can easily be retrieved by sucessively applying our method to each channel along with a fixed reference one, leading to a PNS2 scheme. The method developed here is very simple, easily computable (it requires only a few samples to be effective) and relies on the use of a learning sequence with known spectrum sent before the signal of interest or when it shuts down, by a simple signal injection as an input of the system. It differs from previous methods mainly based on hardware corrections of the sampling devices in order to cancel the desynchronization and return to the unflexible expected uniform grid. We propose here an extended and flexible framework for TI-ADC that adapts itself to imperfect sampling devices. However, the learning sequence used must be known, exactly -as in the case of the cosine waveor at least in mean as in the case of the bandlimited white noise. This could be a drawback of the proposed method if a learning sequence cannot be sent and/or spectrally known. In that purpose an extension of the method can be thought using existing sequences currently used in telecommunications such as Pseudo-Noise Sequences or Communication Pilots. By exploiting the known properties of these sequences (the seed initialization for PN Sequences or the symbols sent for pilots), a calibration method could be derived, allowing to overcome the need of an appropriate learning sequence creation device. Moreover, a blind calibration algorithm is a targeted upgrade of the method, allowing to estimate the delay using directly the samples taken from the signal of interest in bandpass. This will be part of a future work on the method developed here.

7 Fig. 1 :

 71 Fig. 1: Influence of the estimation on the signal reconstruction. (a), (b): Mean square reconstruction error as a function of variance with cosine estimation (red dashed) comparing to the reconstruction without estimation (blue solid) to the low value of N samp = 10, leading to the use of 40 * 10 = 400 samples to converge which is less than the case of N samp = 100 for example (20 * 100 = 2000 samples).

1

 1 Initial error: |b -a| Estimation error: |â -a| After 1 iteration After 2 iterations Final result (∼ 20 iterations) Identity line (b) Nsamp = 100

Fig. 2 :

 2 Fig. 2: Error estimation after algorithm running as a function of initial error (a) For N samp = 10 signal samples (b) For N samp = 100 signal samples

ACKNOWLEDGMENT

This work has been carried out under the financial support of the CNES (French government spatial agency) and Thales Alenia Space.


Franck Silvestre
email: franck.silvestre@irit.fr

Philippe Vidal
email: philippe.vidal@irit.fr

Julien Broisin
email: julien.broisin@irit.fr

Online tests based on contributions provided by teachers and students during faceto-face lectures

Our previous work has introduced the "Tsaap-Notes" platform to increase the motivation and engagement of students in the process of collaborative note taking during lectures. In this paper, we introduce the approach "Notes as Feedback" which consists of recycling interactive questions asked during a lecture in order to semi-automatically build computer based self-assessment tests where feedback provided to students is based on the notes taken by students. A first experimentation on a group of 54 students enrolled in a computer science Master course helped to highlight the benefits of this work: increased participation in note-taking, a massive engagement of students to play the self-assessment tests, and improved student results at the final exam.

Collaborative note taking; audience response system; computer based assessment; self-assessment; feedback I.

INTRODUCTION

Several studies have shown the benefits of using collaborative note taking systems [START_REF] Kam | Livenotes: a system for cooperative and augmented note-taking in lectures[END_REF], micro-blogging systems [START_REF] Junco | The effect of Twitter on college student engagement and grades[END_REF] or audience response systems [START_REF] Caldwell | Clickers in the large classroom: Current research and best-practice tips[END_REF] during lectures. These three kinds of system have their own characteristics: micro-blogging is social-network oriented [START_REF] Kwak | What is Twitter, a social network or a news media?[END_REF] and can be used with any Internet connected devices (laptops, tablets, smartphones, etc.) more and more available in classrooms [START_REF] Ebner | Microblogs in Higher Education-A chance to facilitate informal and processoriented learning?[END_REF]; collaborative note taking systems allow annotation of numeric resources, such as slides, presented during lectures [START_REF] Kam | Livenotes: a system for cooperative and augmented note-taking in lectures[END_REF], [START_REF] Silvestre | Tsaap-Notes--An Open Micro-blogging Tool for Collaborative Notetaking during Faceto-Face Lectures[END_REF]; finally, audience response systems are better known to increase the engagement of the students during a lecture [START_REF] Gauci | Promoting student-centered active learning in lectures with a personal response system[END_REF] and give the teacher opportunities to trigger and arbitrate constructive discussions among students [START_REF] Uhari | Experiences of using an interactive audience response system in lectures[END_REF]. In summary, collaborative construction of knowledge and increased engagement of students are the main advantages given by these systems.

We presented in [START_REF] Silvestre | Tsaap-Notes--An Open Micro-blogging Tool for Collaborative Notetaking during Faceto-Face Lectures[END_REF], Tsaap-Notes, a collaborative note taking platform based on a micro-blogging system and embedding an audience response system. The results of first experimentations on the use of the platform show that combining the features of each system the Tsaap-Notes way reinforces the benefits of each system used separately. More precisely, during the lecture, students take more notes after the presentation of the results obtained on an interactive question asked through the audience response system: the discussion among students and teacher triggered by the presentation of the results, i.e. the feedback from this presentation, is summarised and transcribed by the students in the form of notes.

Some studies [START_REF] Miller | Formative computer based assessment in higher education: The effectiveness of feedback in supporting student learning[END_REF], [START_REF] Ricketts | Improving student performance through computer-based assessment: Insights from recent research[END_REF] show that computer based assessments facilitate the provision of frequent formative assessments to large cohorts of students. Also, the quality of the feedback provided to the students in the context of their work or of their assessment results is a key factor for successful learning [START_REF] Black | Assessment and Classroom Learning[END_REF], [START_REF] Hattie | Assessment and classroom learning: A deductive approach[END_REF], [START_REF] Higgins | The conscientious consumer: reconsidering the role of assessment feedback in student learning[END_REF]. D. Nicol and D. Macfalane-Dick [START_REF] Nicol | Formative assessment and self-regulated learning : A model and seven principles of good feedback practice[END_REF] recommend the use of online tests so that feedback can be accessible anytime, from any place and as many times as students wish.

In this paper, we present our approach called Note as feedback designed to generate online self-assessment tests in a semi-automatic way by recycling the questions asked by the teacher and the notes taken by the students during a lecture. Students can access and run these online tests in the learning management system (LMS) of their institution; the feedback provided by the LMS is based on the notes taken by the students during the lecture.

The paper is organized as follows: section II reviews the main features provided by Tsaap-Notes which the Note as Feedback (NaF) approach is based on; section III shows the motivations for the NaF approach; Section IV presents in detail the design and implementation of the NaF feature in Tsaap-Notes; finally we report a first experimentation with Master students of the University of Toulouse III before concluding and presenting some future work.

II. THE TSAAP-NOTES PLATFORM

Tsaap-Notes has been designed for collaborative annotation of the course material by students during lectures. The platform is presented in detail in [START_REF] Silvestre | Tsaap-Notes--An Open Micro-blogging Tool for Collaborative Notetaking during Faceto-Face Lectures[END_REF], we review in this section only its main features.

Tsaap-Notes is a web application (https://notes.tsaap.eu/tsaap-notes/) compliant with any device able to connect to the Internet (smartphone, laptop, tablets, etc.). Inspired by many web 2.0 and social network applications, each owner of an account on Tsaap-Notes can post a note, put into context a note with hash tags, mark a note as favorite, vote for a particular note or answer directly to a note posted by another user. Furthermore, Tsaap-Notes can easily be embedded in any web tools. For example, Tsaap-Notes has been integrated in a system for online presentation of a course material [START_REF] Silvestre | Tsaap-Notes--An Open Micro-blogging Tool for Collaborative Notetaking during Faceto-Face Lectures[END_REF], allowing students to annotate directly a fine piece of the course material (i.e. a particular slide). Fig. 1. illustrates the user interface of Tsaap-Notes embedded in a web page displaying a slide. The approach Notes as Feedback presented in the next sections is based on two key features of Tsaap-Notes: (1) the ability to gather notes into a same feed, what we called a scope in Tsaap-Notes, and (2) the audience response system. A scope is characterized by a name, a description and a URL (optional). It can be used to reference any kind of learning artifacts: a web resource, a course, an activity, a topic, etc. Any owner of a Tsaap-Notes account can create as many scopes as he wants and can indicate when creating a scope if he is a teacher or a learner around this scope. Fig. 5. illustrates a scope referencing a course hosted in the LMS of the University Toulouse III.

The "Note as question" feature allows a teacher to post a note that is in fact an interactive question. The note must conform to the Moodle Gift format (https://docs.moodle.org/23/en/GIFT_format) in order to be interpreted as a question by the audience response system embedded in Tsaap-Notes. Fig. 2. shows an example of a question written in Gift format. We adopted the Moodle format because our university uses it as LMS; in fact, any other format, such as IMS QTI [START_REF]IMS Question & Test Interoperability Specification[END_REF], could be used to describe a question in Tsaap-Notes. During the lecture, the teacher controls the sequence of the student activity around a question: he decides when to start the survey, when to stop it and when to present the results to the audience. Fig. 3. shows the user interface presented to a student to answer a question while Fig. 4. illustrates the presentation of the results and shows a note taken by a student after this presentation. This note explains the reason why "8" was the good result; in fact, such a note is the transcription of all or only part of the feedback provided to the students after the presentation of the results. Tsaap-Notes, combining an audience response system with a collaborative note taking tool, stimulates [START_REF] Black | Assessment and Classroom Learning[END_REF] constructive interactions between teacher and students after the presentation of the results on an interactive question and (2) the appropriation of this feedback by the students through the note taking. In order to facilitate the preparation of students for their exam, we decided to recycle questions and notes relative to these questions to semi-automatically create online self-assessment tests. The question of feedbacks provided to the student during a computer-based self-assessment is tricky. In traditional online LMS (Moodle, Chamilo, Claroline, Blackboard or any IMS QTI compliant platform), the feedback is, by default, minimalist: for each question, the feedback consists of the score of the student for the current question and of the presentation of the correct answer. If the author of the test takes the trouble to specify additional explanations (general or even for each possible choice) then the LMS is able to provide the students with this additional feedback. This way of managing the feedback raises some issues: (1) the manual completion of the feedback by the teacher for each question is time consuming so that it is rarely done, (2) the feedback provided by the system is the same for all students [START_REF] Bull | Blueprint for computer-assisted assessment[END_REF], (3) the feedback given by the teacher may not be understood by the student because it is not written in the student dialect [START_REF] Chanock | Comments on essays: do students understand what tutors write?[END_REF], [START_REF] Higgins | RETHINKING ASSESSMENT FEEDBACK[END_REF], and finally (4) the feedback is independent of the initial learning context while this characteristic offers guaranties on its quality [START_REF] Bull | Blueprint for computer-assisted assessment[END_REF]. Also, because of the constant increase of students enrolled at the university, the idea of a single teacher providing a quality feedback to each of his students is simply not sustainable [START_REF] Nicol | Formative assessment and self-regulated learning : A model and seven principles of good feedback practice[END_REF]. The use of student productions as feedback has already been explored. For example, in [START_REF] Lea | Computer conferencing and assessment: new ways of writing in higher education[END_REF], messages posted by students on a bulletin board are archived by the teacher to be reused as source of feedback for other students. The experimentations described in [START_REF] Nicol | Peer Instruction versus Class-wide Discussion in large classes : a comparison of two interaction methods in the wired classroom[END_REF] promote the use of audience response system during lectures to build feedback coming either from the teacher or the learners.

The Note as Feedback approach initiated in our work consists of reusing the notes taken by students during a lecture as source of feedback provided to these same students in the context of self-assessment. With this approach (1) the teacher doesn't have to enter the feedback manually (although the teacher is always the indirect source of the feedback), (2) a specific feedback corresponding to what the students transcribed during the lecture is delivered to the students (different lectures addressed to different group will produce different feedbacks to the students of each group), (3) improves the chance that the feedback will be understood by the students because it comes from their own production, written in their dialect, and (4) provides a direct connection between the feedback and the corresponding initial learning context (the initial lecture or activity where the students took notes). In order to help the creation of a self-assessment test based on the interactive questions asked during the lecture, we designed and implemented the "Export questions" feature in Tsaap-Notes. The owner of a scope (the teacher in our case) can export all questions linked to his scope; Fig. 5. illustrates the user interface of Tsaap-Notes allowing the teacher to trigger the export. The export engine finds all questions for the current scope and then, for each question, finds all notes taken by the students on the current processed question. These notes are injected as general feedback in the specification of the question. As mentioned in section II, the export function generates a file that conforms to the Moodle Gift format. Therefore, the generated file can be imported in any Moodle platform through the import function that a teacher can use to populate the question bank of a course. The teacher can modify the specification of an imported question using the edition form provided by Moodle (see Fig. 6.). The field "General feedback" is automatically filled with the notes taken by the students during the initial lecture. So, when the students run a test on Moodle containing such a question, they receive for each question a feedback with the score they obtained on the question, the correct response and the notes they took during the lecture. Fig. 7. shows the user interface provided by Moodle to display the feedback addressed to a student who ran a self-assessment test. The "Notes as feedback" approach gives the teacher the opportunity to reuse the material built by himself (the questions) and by the students (the taken notes) during lectures so that, he has only to select the imported questions coming from Tsaap-Notes to compose the self-assessment test. Also, students can receive a quality feedback, meaning an understandable feedback connected with the lecture they took part in while the teacher don't have to work on it outside the lecture (no need for him to fill complementary explanations for each question in the form edition).

IV. TSAAP-NOTES AND THE GENERATION OF SELF-

The "Note as feedback" system allows the introduction of a computer based self-assessment activity that gives the students the opportunity to work anytime, from anywhere, as many times as they want. Furthermore, these selfassessments add value to the students' engagement during lectures by recycling the notes they took during an activity mainly directed by the teacher.

V. FIRST EXPERIMENTATION

The "Notes as Feedback" system was tested on a group of 54 students enrolled in the first year of a computer science Master course entitled "Developing Applications with Java EE". Out of these 54 students, only 35 were there during the 10 hours of lecture, which is an average rate of 65% of participation. The teacher asked students 82 interactive questions via the Tsaap-Notes platform. 26 students answered the questions, which corresponds to an average rate of 74% of the audience of the lecture.

We show in this section the results of this first experimentation: an increase in the number of notes taken by students on the interactive questions, a large participation in the self-assessment tests, and the improvement of students results at the final exam.

A. Participation in note taking

At the beginning of the experimentation (during the first hour of lecture), the Tsaap-Notes platform was briefly introduced to students. The students were informed that the interactive questions asked by the teacher during the lecture would be reused in self-assessment tests hosted in the Moodle platform. During the first 6 hours, the export feature with the recycling of the notes taken by the students was not available in Tsaap-Notes; therefore, the students were not informed that their notes would be reused in the selfassessment tests. On this first period of the experimentation, students took few notes on the interactive questions: for 55 questions, only 6 notes were posted, which corresponds to a rate of 10%. At the beginning of the seventh hour of lecture, students were informed that the notes they take would be reused in the self-assessment tests. During the 4 last hours of lecture, 27 questions were asked; the students posted 14 notes, which corresponds to a rate of 52%.

The first notable result of this experimentation is that the reuse of notes taken by students in the self-assessment tests significantly strengthened the note taking on the interactive questions: concrete utility of taken notes encouraged students to take notes.

B. Participation in self-assessment tests

Two sets of tests were created on the Moodle workspace corresponding to the course concerned by the experimentation: the first set did not contain any notes taken by the students while in the second set, the notes taken by the students were used as the source of the feedback. Tests without notes where ignored by almost all students: only 4 students ran these tests and then 3 of them switched to second set of tests. 47 students, which correspond to a rate of 87% of the students enrolled in the course, ran the selfassessments tests containing feedback coming from taken notes.

Here is a second notable result: all students prefer running tests with feedback based on their notes, rather than running tests without feedback. We can infer from this observation that students consider as really useful the feedback based on their own taken notes provided during the computer based self-assessment tests.

Let's notice that, in our experimentation, we did not consider creating a set of tests with feedback entered by the teacher. This option has been intentionally discarded because our goals consist of (1) addressing issues coming from this traditional approach where the teacher enter the feedback for each question (cf. section III: the cost of manual specification of the feedback and the risk of an inappropriate feedback, etc.), and (2) increasing the engagement of students in the note taking process by giving value to their production.

C. Results in the final exam

At the end of the course, a test containing 102 questions and counting for 30% of the final grade was submitted to the students. In these 102 questions, 82 questions came from Tsaap-Notes. The numerical values in this set of questions were modified in order to limit the rote learning effect. The results in 2014 were radically different from those obtained in the previous year (the course in its actual form has only been existing for two years): the average mark in the test was 17/20 with a standard deviation of 1.48 (Fig. 8. illustrates the distribution of the grades in 2014), while the average ones in the previous year was 11.92 with a standard deviation of 3.26. The system used in the context of our teaching, which integrates the platform Tsaap-Notes and a set of selfassessment tests, has led to a remarkable increase in student performance on the computer based assessment at the final exam. The comparison of the results above, however, must be tempered by the significant differences presented by the two summative assessments: in 2013, the test consisted of 54 questions only (102 in 2014) and only 20 questions were common to both exams. Also, it is hard to distinguish, in the system, what had the strongest influence: in 2013, the Tsaap-Notes platform was not integrated within the teaching, and the self-assessment tests were not available to students.

VI. CONCLUSION AND PERSPECTIVES

The Tsaap-Notes platform combines micro-blogging features with audience response system in order to foster collaborative note taking by students during lectures. Especially, Tsaap-Notes gives the students the opportunity to take notes as a whole or to focus on a specific part of the course material such as a slide or an interactive question.

In this paper, we presented the new feature called "Notes as feedback" which consists of recycling the questions and notes produced in Tsaap-Notes in order to semiautomatically generate computer based self-assessment tests. The tedious task of creating such test is now limited: teachers only have to create the test; they don't have to elaborate the questions that make up the test. These tests, carried out in a learning management system such as Moodle, provide the students a feedback based on the notes previously taken by these students.

The results coming from the first experimentation are encouraging: (1) students are more engaged in note taking when these notes are reused in self-assessment tests; (2) selfassessment tests resulting from the "Notes as feedback" approach are massively played by the students; (3) the implementation of the whole system (Tsaap-Notes and selfassessment tests) has a very positive impact on the results of the students in their final computer based assessment.

These results lead us to continue our research on semiautomatic generation of computer based assessment tests reusing student notes as the source of feedback. The approach developed in Tsaap-Notes is a first step in the personalization of computer based self-assessment tests. Indeed, the tests generated from Tsaap-Notes are built with questions asked by the teacher during lectures and the results and answers of each student are recorded. The notes taken by the students on the displayed results for these questions are recorded too. All these elements could be used to provide each student with a personalized set of tests taking into account his profile. In the tests generated by Tsaap-Notes, the feedback is already more than a generic production identical for all students: the students, in the context of lectures they participate in, build the feedback. While this contextualization of the feedback corresponds only to a group level adaptation (a group of students participating in the same lecture), some research could allow us to adapt the feedback at each person's level inside the group. In our current work, we try to answer the following questions: how to build a student profile in the situation of self-assessment? How to extract from the elements recorded in Tsaap-Notes the relevant information to build personalized tests? Which algorithms and recommendation mechanisms should be implemented?

Figure 1 .

 1 Figure 1. Tsaap-Notes embedded in web page displaying a slide

Figure 2 .

 2 Figure 2. Edition of a question following the Moodle Gift format

Figure 3 .

 3 Figure 3. User interface to submit an answer

Figure 4 .

 4 Figure 4. Presentation of the results with feedback transcription

Figure 5 .

 5 Figure 5. Export of the questions relative to a scope

Figure 6 .Figure 7 .

 67 Figure 6. Edition in Moodle of a question imported from Tsaap-Notes

Figure 8 .

 8 Figure 8. Distribution of grades in the computer based assessment in 2014