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On the Moments and Tails of the Spectrum of an FM Wave
Author(s) -
Blachman Nelson M.
Publication year - 1969
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/rs004i005p00437
Subject(s) - moment (physics) , mathematics , spectrum (functional analysis) , spectral density , central moment , second moment of area , standard deviation , distribution (mathematics) , mathematical analysis , spectral power distribution , physics , random variable , statistics , optics , moment generating function , classical mechanics , quantum mechanics , geometry
The first three moments of the normalized spectrum of an FM wave equal the corresponding moments of the distribution of instantaneous frequency deviations. The fourth spectral moment contains an additional term given by the product of the mean‐squared deviation times the second moment of the normalized modulating spectrum. These moments are used to bound the power in the spectral tails.