Abstract
The use of complex demodulation techniques, where a frequency band of interest in a given time series is shifted to zero and then low pass filtered, is discussed. Instantaneous values of signal phase and amplitude are derived from the complex demodulates and cross spectra can be estimated from averages of their products. The technique is discussed with particular reference to the geomagnetic field; the instantaneous properties of the magnetic field fluctuations yielding information concerning the non stationary properties of hydromagnetic waves (the wave polarization parameters). Cross spectral determinations can be used to produce transfer functions which enable the response of the Earth to be estimated for variations of different frequencies. Complex demodulation enables a selection criteria to be applied so that more reliable values of the transfer function may be computed.
Analyse
L’utilisation de techniques de démodulation complexe par lesquelles une bande de fréquence dans une série temporelle donnée est décalée vers les fréquences nulles puis analysée au travers d’un filtre passebas est discutée. Des valeurs instantanées de l’amplitude et de la phase du signal sont tirées des signaux démodulés complexes, et des spectres croisés peuvent être estimés à partir de moyennes de leurs produits. La technique est discutée, dans le cadre particulier de l’étude du champ géométrique, les propriétés instantanées des fluctuations du champ donnant des informations sur les caractéristiques non stationnaires des ondes hydromagnétiques (paramètre de polarisation des ondes). Les déterminations de spectres croisés peuvent être utilisées pour obtenir les fonctions de transfert permettant d’évaluer la réponse de la Terre à des fluctuations de fréquences différentes. La démodulation complexe permet d’appliquer des critères de sélection pour pouvoir calculer avec une plus grande fiabilité, les valeurs de la fonction de transfert.
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Webb, D.C. The analysis of non stationary data using complex demodulation. Ann. Telecommun. 34, 131–137 (1979). https://doi.org/10.1007/BF03004189
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DOI: https://doi.org/10.1007/BF03004189