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Predictive spectral analysis of short records using maximum entropy

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Пре¶rt;ложен сnособ сnекmрaльного aнaлuзa, основaнняыŭ нa nре¶rt;скaзaнuu сuгнaлa с nомощью aвmорегрессuонных naрaмеmров. Эmоm сnособ являеmся ¶rt;aльнеŭшuм рaзвumuем клaссuческuх мзmо¶rt;ов сnекmрaльного aнaлuзa с nрuвлеченuем u¶rt;еŭ uз меmо¶rt;a мaксuмaльноŭ энmроnuu. Сnособ облa¶rt;aеm nовышенноŭ рaэрешaющеŭ сnособносmью nо срaвненuю с клaссuческuмu меmо¶rt;aмu nрu aнaлuэе nроцессов с ¶rt;осmamочно хорошuм оmношенuем сuгнaл шум. Сnекmр мощносmu сuгнaлов оnре¶rt;еляеmср более нa¶rt;ежно, чем в меmо¶rt;е мaксuмaльноŭ энmроnuu. Воmлuчuе оm меmо¶rt;a мaксuмaльноŭ энmроnuu nре¶rt;ложенныŭ сnособ сnекmрaльного aнaлuзa nозволяеm оnре¶rt;еляmь mоже фaзовыŭ сnекmр сuгнaлов. Пaрaмеmры nре¶rt;скaзывaющего фuльmрa вычuсляюmся меmо¶rt;ом нauменьшuх квa¶rt;рamов, в коmором uсnользовaнa регулярuзaцuя ¶rt;ля вы¶rt;еленuя усmоŭчuвых облaсmеŭ решенuя.

Summary

A method of spectral analysis based on the prediction of the signal by means of AR parameters is proposed. The essence of this method ranks it between the classical methods of spectral analysis and the method of maximum entropy. For sufficiently high SNR its resolution is higher than that of the classical methods. The new method enables power and phase spectra of the signal to be determined, and provides a better determination of the power spectrum amplitude. than the method of maximum entropy. A regularization procedure is presented which abolished the instability of the prediction filter, obtained by the least-squares method.

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Konopásková, J. Predictive spectral analysis of short records using maximum entropy. Stud Geophys Geod 29, 228–237 (1985). https://doi.org/10.1007/BF01638434

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