R. Yager, A new approach to the summarization of data, Information Sciences, vol.28, issue.1, pp.69-86, 1982.
DOI : 10.1016/0020-0255(82)90033-0

L. Zadeh, A computational approach to fuzzy quantifiers in natural languages, Computers & Mathematics with Applications, vol.9, issue.1, pp.149-184, 1983.
DOI : 10.1016/0898-1221(83)90013-5

J. Kacprzyk and S. Zadrozny, Protoforms of linguistic data summaries: towards more general naturallanguage-based data mining tools, in: Soft computing systems, pp.417-425, 2002.

J. Lafler and T. D. Kinman, The calculation of RR Lyrae periods by electronic computer, The Astrophysical Journal Supplement Series, vol.11, issue.216, 1965.

C. E. Goldblum, R. C. Ritter, and G. T. Gillies, Using the fast Fourier transform to determine the period of a physical oscillator with precision, Review of Scientific Instruments, vol.59, issue.5, p.778, 1988.
DOI : 10.1063/1.1139828

V. Backmutsky, J. Blaska, and M. Sedlacek, Methods of finding actual signal period time, Proc. of IMEKO'00, pp.243-248, 2000.

A. M. Noll, Cepstrum Pitch Determination, The Journal of the Acoustical Society of America, vol.41, issue.2, 1967.
DOI : 10.1121/1.1910339

Z. Li, Mining periodicity and object relationship in spatial and temporal data, 2013.

M. J. Costa, B. Finkenstädt, P. D. Gould, J. Foreman, K. J. Halliday et al., Estimating periodicity of oscillatory time series through resampling techniques, 2011.

M. G. Geers and V. G. Kouznetsova, Scale transitions in solid mechanics based on computational homogenization, Mechanics, vol.27, pp.37-48, 2001.

R. U. Kiran and M. Kitsuregawa, Novel Techniques to Reduce Search Space in Periodic-Frequent Pattern Mining, Proc. of DSAA'14, pp.377-391, 2014.
DOI : 10.1007/978-3-319-05813-9_25

P. Grosche and M. Muller, Computing predominant local periodicity information in music recordings, 2009 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, pp.33-36, 2009.
DOI : 10.1109/ASPAA.2009.5346544

J. Duval, P??riodes locales et propagation de p??riodes dans un mot, Theoretical Computer Science, vol.204, issue.1-2, pp.87-98, 1998.
DOI : 10.1016/S0304-3975(98)00033-4

G. Moyse, M. Lesot, and B. Bouchon-meunier, Linguistic summaries for periodicity detection based on mathematical morphology, 2013 IEEE Symposium on Foundations of Computational Intelligence (FOCI), pp.106-113, 2013.
DOI : 10.1109/FOCI.2013.6602462
URL : https://hal.archives-ouvertes.fr/hal-00932852

J. Kacprzyk and S. Zadrozny, Computing With Words Is an Implementable Paradigm: Fuzzy Queries, Linguistic Data Summaries, and Natural-Language Generation, IEEE Transactions on Fuzzy Systems, vol.18, issue.3, pp.461-472, 2010.
DOI : 10.1109/TFUZZ.2010.2040480

B. Bouchon-meunier and G. Moyse, Fuzzy linguistic summaries: Where are we, where can we go?, 2012 IEEE Conference on Computational Intelligence for Financial Engineering & Economics (CIFEr), pp.317-324, 2012.
DOI : 10.1109/CIFEr.2012.6327810
URL : https://hal.archives-ouvertes.fr/hal-00932854

J. Kacprzyk and R. Yager, ???Softer??? optimization and control models via fuzzy linguistic quantifiers, Information Sciences, vol.34, issue.2, pp.157-178, 1984.
DOI : 10.1016/0020-0255(84)90022-7

J. Kacprzyk and A. Wilbik, Towards an efficient generation of linguistic summaries of time series using a degree of focus, NAFIPS 2009, 2009 Annual Meeting of the North American Fuzzy Information Processing Society, pp.1-6, 2009.
DOI : 10.1109/NAFIPS.2009.5156430

J. Kacprzyk and R. Yager, LINGUISTIC SUMMARIES OF DATA USING FUZZY LOGIC, International Journal of General Systems, vol.1, issue.2, pp.133-154, 2001.
DOI : 10.1016/0898-1221(83)90013-5

F. Díaz-hermida, A. Ramos-soto, and A. Bugarín, On the role of fuzzy quantified statements in linguistic summarization of data, 2011 11th International Conference on Intelligent Systems Design and Applications, pp.166-171, 2011.
DOI : 10.1109/ISDA.2011.6121649

R. Castillo-ortega, N. Marín, D. Sánchez, and A. Tettamanzi, Quality Assessment in Linguistic Summaries of Data, Proc. of IPMU'12, pp.285-294, 2012.
DOI : 10.1007/978-3-642-31715-6_31

L. Danlos, F. Meunier, and V. Combet, EasyText: an operational NLG system, Proc. of ENLG'11, pp.139-144, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00614760

P. Cariñena, A. Bugarín, M. Mucientes, and S. Barro, A language for expressing fuzzy temporal rules, Mathware & soft computing, vol.7, issue.2, pp.213-227, 2000.

R. Castillo-ortega, N. Marín, D. Sánchez, E. Corchado, and H. Yin, Fuzzy Quantification-Based Linguistic Summaries in Data Cubes with Hierarchical Fuzzy Partition of Time Dimension, Intelligent Data Engineering and Automated Learning, pp.578-585, 2009.
DOI : 10.1016/0898-1221(83)90013-5

J. Kacprzyk, A. Wilbik, and S. Zadrozny, Linguistic summarization of time series using a fuzzy quantifier driven aggregation, Fuzzy Sets and Systems, pp.1485-1499, 2008.

A. Ramos-soto, A. Bugarín, S. Barro, and F. Díaz-hermida, Automatic linguistic descriptions of meteorological data, Proc. of the Iberian Conf. on Information Systems and Technologies'13, pp.1-6, 2013.

G. Moyse, M. Lesot, and B. Bouchon-meunier, Mathematical Morphology Tools to Evaluate Periodic Linguistic Summaries, Proc. of FQAS'13, pp.257-268, 2013.
DOI : 10.1007/978-3-642-40769-7_23
URL : https://hal.archives-ouvertes.fr/hal-00932844

D. Gerhard, Pitch extraction and fundamental frequency: history and current techniques, 2003.

B. Kedem, Spectral analysis and discrimination by zero-crossings, Proceedings of the IEEE, vol.74, issue.11, pp.1477-1493, 1986.
DOI : 10.1109/PROC.1986.13663

M. Tsuji and E. Yamada, A wavelet approach to real time estimation of power system frequency, Proc. of SICE'01, pp.58-65, 2001.

M. K. Mahmood, J. E. Allos, and M. A. Karim, Microprocessor Implementation of a Fast and Simultaneous Amplitude and Frequency Detector for Sinusoidal Signals, IEEE Transactions on Instrumentation and Measurement, vol.34, issue.3, pp.413-417, 1985.
DOI : 10.1109/TIM.1985.4315360

A. M. Zayezdny, Y. Adler, and I. Druckmann, Short time measurement of frequency and amplitude in the presence of noise, IEEE Transactions on Instrumentation and Measurement, vol.41, issue.3, pp.397-402, 1992.
DOI : 10.1109/19.153336

D. Sánchez and G. Triviño, Computational perceptions of uninterpretable data. A case study on the linguistic modeling of human gait as a quasi-periodic phenomenon, Fuzzy Sets and Systems, pp.101-121, 2013.

L. Palmer, Coarse frequency estimation using the discrete Fourier transform (Corresp.), IEEE Transactions on Information Theory, vol.20, issue.1, pp.104-109, 1974.
DOI : 10.1109/TIT.1974.1055156

B. Quinn, Estimating frequency by interpolation using Fourier coefficients, IEEE Transactions on Signal Processing, vol.42, issue.5, pp.1264-1268, 1994.
DOI : 10.1109/78.295186

P. J. Kootsookos, A review of the frequency estimation and tracking problems, Tech. rep., Australian National University, 1993.

E. Jacobsen and P. J. Kootsookos, Fast, Accurate Frequency Estimators [DSP Tips & Tricks], IEEE Signal Processing Magazine, vol.24, issue.3, pp.123-125, 2007.
DOI : 10.1109/MSP.2007.361611

B. Bernd, U. Ligges, and C. Weihs, Frequency estimation by DFT interpolation: a comparison of methods, 2009.

D. Gabor, Theory of communication. Part 1: The analysis of information, Journal of the Institution of Electrical Engineers - Part III: Radio and Communication Engineering, vol.93, issue.26, pp.439-441, 1946.
DOI : 10.1049/ji-3-2.1946.0074

J. Allen and L. Rabiner, A unified approach to short-time Fourier analysis and synthesis, Proceedings of the IEEE, vol.65, issue.11, pp.1558-1564, 1977.
DOI : 10.1109/PROC.1977.10770

A. Grossmann and J. Morlet, Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape, SIAM Journal on Mathematical Analysis, vol.15, issue.4, pp.723-736, 1984.
DOI : 10.1137/0515056

S. Mallat, A theory for multiresolution signal decomposition: the wavelet representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.11, issue.7, pp.674-693, 1989.
DOI : 10.1109/34.192463

N. Huang, Z. Shen, S. Long, M. Wu, H. Shih et al., The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.454, issue.1971, pp.903-995, 1971.
DOI : 10.1098/rspa.1998.0193

H. Ke, K. Wang, C. Yang, and K. Chang, Wavelet and Hilbert-Huang transform based on predicting stock forecasting in second-order autoregressive mode, Int, Journal of Applied Physics and Mathematics, vol.4, issue.1, pp.9-14, 2014.

G. Rilling, P. Flandrin, and P. Goncalves, On empirical mode decomposition and its algorithms, Proc. of NSIP'03, pp.8-11, 2003.
URL : https://hal.archives-ouvertes.fr/inria-00570628

F. Cong, T. Sipola, T. Huttunen-scott, X. Xu, T. Ristaniemi et al., Hilbert-Huang versus Morlet wavelet transformation on mismatch negativity of children in uninterrupted sound paradigm, Nonlinear Biomedical Physics, vol.3, issue.1
DOI : 10.1186/1753-4631-3-1

N. Padmaja and S. Varadarajan, Atmospheric signal processing using wavelets and HHT, Journal of Computations & Modelling, vol.1, issue.1, pp.17-30, 2011.

M. Vlachos, P. S. Yu, and V. Castelli, On Periodicity Detection and Structural Periodic Similarity, Proc. of SIAM'05, pp.449-460, 2005.
DOI : 10.1137/1.9781611972757.40

S. Papadimitriou, A. Brockwell, and C. Faloutsos, Adaptive, Hands-Off Stream Mining, Proc. of VLDB'03, pp.560-571, 2003.
DOI : 10.1016/B978-012722442-8/50056-2

E. Keogh, K. Chakrabarti, M. Pazzani, and S. Mehrotra, Dimensionality Reduction for Fast Similarity Search in Large Time Series Databases, Knowledge and Information Systems, vol.3, issue.3, pp.263-286, 2001.
DOI : 10.1007/PL00011669

E. Keogh, K. Chakrabarti, S. Mehrotra, and M. Pazzani, Locally adaptive dimensionality reduction for indexing large time series databases, ACM Trans. on Database Systems, vol.27, issue.2, pp.188-228, 2002.

Y. Cai and R. Ng, Indexing spatio-temporal trajectories with Chebyshev polynomials, Proceedings of the 2004 ACM SIGMOD international conference on Management of data , SIGMOD '04, pp.1-12, 2004.
DOI : 10.1145/1007568.1007636

B. Ozden, S. Ramaswamy, and A. Silberschatz, Cyclic association rules, Proceedings 14th International Conference on Data Engineering, pp.412-421, 1998.
DOI : 10.1109/ICDE.1998.655804

R. Agrawal and R. Srikant, Mining sequential patterns, Proceedings of the Eleventh International Conference on Data Engineering, pp.3-14, 1995.
DOI : 10.1109/ICDE.1995.380415

C. Lee, M. Chen, and C. Lin, Progressive partition miner: an efficient algorithm for mining general temporal association rules, IEEE Trans. on Knowledge and Data Engineering, vol.15, issue.4, pp.1004-1017, 2003.

N. Méger and C. Rigotti, Constraint-Based Mining of Episode Rules and Optimal Window Sizes, Proc. of PKDD'04, pp.313-324, 2004.
DOI : 10.1007/978-3-540-30116-5_30

C. Berberidis, I. P. Vlahavas, W. G. Aref, M. J. Atallah, and A. K. Elmagarmid, On the Discovery of Weak Periodicities in Large Time Series, Proc. of PKDD'02, pp.51-61, 2002.
DOI : 10.1007/3-540-45681-3_5

S. Ma and J. L. Hellerstein, Mining Partially Periodic Patterns With Unknown Periods From Event Stream, Proc. of ICDE'01, pp.205-214, 2001.
DOI : 10.1007/978-1-4613-0231-5_15

G. Moyse and M. Lesot, Fast and Incremental Computation for the Erosion Score, Proc. of IPMU'14, pp.376-385, 2014.
DOI : 10.1007/978-3-319-08795-5_39

J. Serra, Introduction to mathematical morphology, Computer Vision, Graphics, and Image Processing, vol.35, issue.3, pp.283-305, 1986.
DOI : 10.1016/0734-189X(86)90002-2

S. Gorard, REVISITING A 90-YEAR-OLD DEBATE: THE ADVANTAGES OF THE MEAN DEVIATION, British Journal of Educational Studies, vol.30, issue.1, pp.417-430, 2005.
DOI : 10.1080/0307507032000058064

M. Basseville and I. Nikiforov, Detection of abrupt changes: theory and application, 1993.
URL : https://hal.archives-ouvertes.fr/hal-00008518

R. Castillo-ortega, D. Sánchez, and N. Marín, Time series comparison using linguistic fuzzy techniques, Computational Intelligence for Knowledge-Based Systems Design, pp.6178-330, 2010.

R. Moore, Interval arithmetic and automatic error analysis in digital computing, 1963.

A. Appendix, Determination of P (d = ?|n, g) Denoting d the random variable measuring the absolute deviation of the sizes of g groups containing n points, we compute in this section P (d = ? |n, g ), the probability that d equals ? given n and g. This probability is defined only if n ? g and g ? 1. The proof is split in two parts. First, a general expression for d is given allowing its computation by decomposing the group sizes into two, the ones whose size is smaller than