{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:35:07Z","timestamp":1760243707695,"version":"build-2065373602"},"reference-count":50,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2012,8,8]],"date-time":"2012-08-08T00:00:00Z","timestamp":1344384000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Abstract: This article first introduces the concept of wavelet q-Fisher information and then derives a closed-form expression of this quantifier for scaling signals of parameter \u03b1. It is shown that this information measure appropriately describes the complexities of scaling signals and provides further analysis flexibility with the parameter q. In the limit of q \u2192 1, wavelet q-Fisher information reduces to the standard wavelet Fisher information and for q &gt; 2 it reverses its behavior. Experimental results on synthesized fGn signals validates the level-shift detection capabilities of wavelet q-Fisher information. A comparative study also shows that wavelet q-Fisher information locates structural changes in correlated and anti-correlated fGn signals in a way comparable with standard breakpoint location techniques but at a fraction of the time. Finally, the application of this quantifier to H.263 encoded video signals is presented.<\/jats:p>","DOI":"10.3390\/e14081478","type":"journal-article","created":{"date-parts":[[2012,8,8]],"date-time":"2012-08-08T12:25:01Z","timestamp":1344428701000},"page":"1478-1500","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Wavelet q-Fisher Information for Scaling Signal Analysis"],"prefix":"10.3390","volume":"14","author":[{"given":"Julio","family":"Ram\u00edrez-Pacheco","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, CINVESTAV-IPN Guadalajara Unit, 45019 Zapop\u00e1n, Jalisco, Mexico"},{"name":"Department of Basic Sciences and Engineering (DCBeI), University of Caribe, 77528, Canc\u00fan, Q.Roo, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Deni","family":"Torres-Rom\u00e1n","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, CINVESTAV-IPN Guadalajara Unit, 45019 Zapop\u00e1n, Jalisco, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jes\u00fas","family":"Argaez-Xool","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, CINVESTAV-IPN Guadalajara Unit, 45019 Zapop\u00e1n, Jalisco, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luis","family":"Rizo-Dominguez","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences and Engineering (DCBeI), University of Caribe, 77528, Canc\u00fan, Q.Roo, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joel","family":"Trejo-Sanchez","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences and Engineering (DCBeI), University of Caribe, 77528, Canc\u00fan, Q.Roo, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francisco","family":"Manzano-Pinz\u00f3n","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences and Engineering (DCBeI), University of Caribe, 77528, Canc\u00fan, Q.Roo, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,8,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/90.282603","article-title":"On the self-similar nature of ethernet traffic (extended version)","volume":"2","author":"Leland","year":"1994","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1109\/90.392383","article-title":"Wide area traffic: The failure of poisson modeling","volume":"3","author":"Paxson","year":"1995","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.comcom.2005.02.004","article-title":"Stochastic processes for computer network traffic modelling","volume":"29","author":"Lee","year":"2005","journal-title":"Comput. Commun."},{"key":"ref_4","first-page":"404","article-title":"Statistical methods for data with long-range dependence","volume":"7","author":"Beran","year":"1992","journal-title":"Stat. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1566","DOI":"10.1109\/26.380206","article-title":"Long-range dependence in variable-bit-rate video traffic","volume":"43","author":"Beran","year":"1995","journal-title":"IEEE Trans. Commun."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1109\/65.967596","article-title":"MPEG-4 and H.263 video traces for network performance evaluation","volume":"15","author":"Fitzek","year":"2001","journal-title":"IEEE Netw."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2111","DOI":"10.1016\/j.sigpro.2007.02.010","article-title":"Robust estimation of the self-similarity parameter in network traffic using the wavelet transform","volume":"87","author":"Shen","year":"2007","journal-title":"Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1016\/j.comnet.2004.11.017","article-title":"On the wavelet spectrum diagnostic for Hurst parameter estimation in the analysis of internet traffic","volume":"48","author":"Stoev","year":"2005","journal-title":"Comput. Netw."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1049\/el.2010.7167","article-title":"Cosh window behaviour of wavelet Tsallis q-entropies in \n\t\t\t\t\t\t\t          \n\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t              1\n\t\t\t\t\t\t\t              \/\n\t\t\t\t\t\t\t              \n\t\t\t\t\t\t\t                f\n\t\t\t\t\t\t\t                \u03b1\n\t\t\t\t\t\t\t              \n\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t          \n\t\t\t\t\t\t\t         signals","volume":"47","year":"2011","journal-title":"Electron. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1007\/s004249900135","article-title":"Physiological time series: Distinguishing fractal noises and motions","volume":"439","author":"Eke","year":"2000","journal-title":"Pflugers Arch."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1016\/S0378-4371(96)00386-X","article-title":"Tsallis nonextensive themostatistics and Fisher\u2019s information measure","volume":"235","author":"Plastino","year":"1997","journal-title":"Phys. A"},{"key":"ref_12","unstructured":"Samorodnitsky, G., and Taqqu, M. (1994). Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance, Chapman & Hall\/CRC Press."},{"key":"ref_13","unstructured":"Beran, J. (1994). Statistics for Long-Memory Processes, Chapman & Hall\/CRC Press."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1049\/el:20092638","article-title":"Sub-pHz MOSFET 1\/f noise measurements","volume":"45","author":"Mandal","year":"2009","journal-title":"Electron. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2770","DOI":"10.1016\/j.physa.2010.02.044","article-title":"Use and misuse of some Hurst parameter estimators applied to stationary and non-stationary financial time series","volume":"389","author":"Serinaldi","year":"2010","journal-title":"Phys Stat Mech Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/S0378-3758(98)00249-3","article-title":"Self-affine time series: Measures of weak and strong persistence","volume":"80","author":"Malamud","year":"1999","journal-title":"J. Statist. Plann. Inference"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1007\/BF02083489","article-title":"Estimating the fractal dimension of profiles: A comparison of methods","volume":"26","author":"Gallant","year":"1994","journal-title":"Math. Geol."},{"key":"ref_18","first-page":"1","article-title":"Distinguishing stationary\/nonstationary scaling processes using wavelet Tsallis q-entropies","volume":"2012","year":"2012","journal-title":"Math. Probl. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1648","DOI":"10.3390\/e13091648","article-title":"Wavelet Fisher\u2019s information of \n\t\t\t\t\t\t\t\t          \n\t\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t\t              1\n\t\t\t\t\t\t\t\t              \/\n\t\t\t\t\t\t\t\t              \n\t\t\t\t\t\t\t\t                f\n\t\t\t\t\t\t\t\t                \u03b1\n\t\t\t\t\t\t\t\t              \n\t\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t\t          \n\t\t\t\t\t\t\t\t         signals","volume":"13","year":"2011","journal-title":"Entropy"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/jae.659","article-title":"Computation and analysis of multiple structural change models","volume":"18","author":"Bai","year":"2003","journal-title":"J. Appl. Econom."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"S289","DOI":"10.1088\/0026-1394\/40\/3\/308","article-title":"Stochastic models and statistical analysis for clock noise","volume":"40","author":"Percival","year":"2003","journal-title":"Metrologia"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1137\/1010093","article-title":"Fractional Brownian motions, fractional noises and applications","volume":"10","author":"Mandelbrot","year":"1968","journal-title":"SIAM Rev."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"910","DOI":"10.1109\/18.119751","article-title":"Wavelet analysis and synthesis of fractional Brownian motion","volume":"38","author":"Flandrin","year":"1992","journal-title":"IEEE Trans. Inform. Theor."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1142\/S0218348X95000151","article-title":"Estimation and simulation of fractal stochastic point processes","volume":"3","author":"Lowen","year":"1995","journal-title":"Fractals"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3279","DOI":"10.1103\/PhysRevLett.71.3279","article-title":"Wavelet transforms and atmospheric turbulence","volume":"71","author":"Hudgins","year":"1993","journal-title":"Phys. Rev. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1109\/5.488697","article-title":"Wavelets: The mathematical background","volume":"84","author":"Cohen","year":"1996","journal-title":"Proc. IEEE"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1109\/18.650984","article-title":"Wavelet analysis of long-range dependent traffic","volume":"44","author":"Abry","year":"1998","journal-title":"IEEE Trans. Inform. Theor."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"878","DOI":"10.1109\/18.761330","article-title":"A wavelet based joint estimator of the parameters of long-range dependence","volume":"45","author":"Veitch","year":"1999","journal-title":"IEEE Trans. Inform. Theor."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"991","DOI":"10.1109\/18.992817","article-title":"Statistical study of the wavelet analysis of fractional brownian motion","volume":"48","author":"Bardet","year":"2002","journal-title":"IEEE Trans. Inform. Theor."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/S0165-1684(98)00240-0","article-title":"Statistical properties of the wavelet decomposition of certain non-Gaussian self-similar processes","volume":"75","year":"1999","journal-title":"Signal Process."},{"key":"ref_31","first-page":"173","article-title":"Fisher\u2019s information and the analysis of complex signals","volume":"256","author":"Martin","year":"1999","journal-title":"Phys. Stat. Mech. Appl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1016\/S0378-4371(00)00531-8","article-title":"Fisher information and non-linear dynamics","volume":"291","author":"Martin","year":"2001","journal-title":"Phys. Stat. Mech. Appl."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1016\/j.physa.2004.12.041","article-title":"Fisher information measure of geoelectrical signals","volume":"351","author":"Telesca","year":"2005","journal-title":"Phys. Stat. Mech. Appl."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"468","DOI":"10.1016\/j.cplett.2005.08.032","article-title":"The Fisher information of single-particle systems with a central potential","volume":"414","author":"Romera","year":"2005","journal-title":"Chem. Phys. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1023\/A:1011080128419","article-title":"Quantum Fisher information and uncertainty relation","volume":"53","author":"Luo","year":"2000","journal-title":"Lett. Math. Phys."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/S0375-9601(03)00570-X","article-title":"Analysis of signals in the Fisher\u2013Shannon information plane","volume":"312","author":"Vignat","year":"2003","journal-title":"Phys. Lett. A"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2644","DOI":"10.1103\/PhysRevE.49.2644","article-title":"Spectral 1\/f noise derived from extremized physical information","volume":"49","author":"Frieden","year":"1994","journal-title":"Phys. Rev. E"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1016\/j.physa.2005.09.060","article-title":"Wavelet entropy and fractional Brownian motion time series","volume":"365","author":"Perez","year":"2006","journal-title":"Phys. Stat. Mech. Appl."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1016\/j.physa.2006.12.057","article-title":"Wavelet entropy of stochastic processes","volume":"379","author":"Zunino","year":"2007","journal-title":"Phys. Stat. Mech. Appl."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"111","DOI":"10.3390\/e11010111","article-title":"Generalized complexity and classical quantum transition","volume":"11","author":"Kowalski","year":"2009","journal-title":"Entropy"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/s004220000212","article-title":"Wavelet entropy in event-related potentials: A new method shows ordering of EEG oscillations","volume":"84","author":"Quiroga","year":"2001","journal-title":"Biol. Cybern."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.physa.2004.03.082","article-title":"A possible deformed algebra and calculus inspired in nonextensive thermostatistics","volume":"340","author":"Borges","year":"2004","journal-title":"Phys. Stat. Mech. Appl."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"R1","DOI":"10.1088\/0967-3334\/23\/1\/201","article-title":"Fractal characterization of complexity in temporal physiological signals","volume":"23","author":"Eke","year":"2002","journal-title":"Physiol. Meas."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1016\/j.jmp.2006.07.004","article-title":"Fractal analyses of short time series: A re-assessment of classical methods","volume":"50","author":"Deligneres","year":"2006","journal-title":"J. Math. Psychol."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"675","DOI":"10.1109\/TBME.2008.2005949","article-title":"Local scale exponents of blood pressure and heart rate variability by detrended fluctuation analysis: Effects of posture, exercise and aging","volume":"56","author":"Castiglioni","year":"2009","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"033126","DOI":"10.1063\/1.2976187","article-title":"A blind method for the estimation of the Hurst exponent in time series: Theory and methods","volume":"18","author":"Esposti","year":"2008","journal-title":"Chaos"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1441","DOI":"10.1016\/j.matcom.2010.06.007","article-title":"Long-memory or shifting means in geophysical time series?","volume":"81","author":"Rea","year":"2011","journal-title":"Math. Comput. Simulat."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/j.matcom.2008.01.041","article-title":"Detecting multiple mean breaks at unknown points with Atheoretical Regression Trees","volume":"78","author":"Capelli","year":"2008","journal-title":"Math. Comput. Simulat."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1093\/biomet\/74.1.95","article-title":"Tests for Hurst effect","volume":"74","author":"Davies","year":"1987","journal-title":"Biometrika"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"606","DOI":"10.1016\/S0378-4371(97)00252-5","article-title":"Evaluating scaled windowed variance for estimating the hurst coefficient of time series","volume":"241","author":"Cannon","year":"1996","journal-title":"Phys. Stat. Mech. Appl."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/8\/1478\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:51:41Z","timestamp":1760219501000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/8\/1478"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,8,8]]},"references-count":50,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2012,8]]}},"alternative-id":["e14081478"],"URL":"https:\/\/doi.org\/10.3390\/e14081478","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2012,8,8]]}}}