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- W1569684943 abstract "The concepts of instantaneous amplitude and frequency appear quite natural to those who use amplitude or frequency modulations. However, the precise and unambiguous definition of these quantities presents numerous problems that have intrigued researchers for quite some time already and continue to do so. After having presented the problem in a relatively elementary fashion, we show the contradictions that present themselves in most apparently obvious definitions that have been given. The definition that seems to avoid these contradictions the best is based on the use of the analytic signal, and the following discussion presents the main consequences of the use of this tool to unambiguously define the instantaneous amplitude, phase and frequency of a signal. The results are relatively simple to understand as far as amplitude is concerned. Therefore, we analyze in considerably more detail the problems related to instantaneous phase. We show in particular that the so-called phase signals, that is, signals whose instantaneous amplitude is constant, must satisfy fairly subtle conditions. These conditions are related to the properties of complex functions that must simultaneously have a modulus equal to one and be analytic on a complex semi-plane, which introduces in particular Blaschke functions. The main physical consequences of these properties are analyzed." @default.
- W1569684943 created "2016-06-24" @default.
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- W1569684943 date "2008-01-01" @default.
- W1569684943 modified "2023-09-23" @default.
- W1569684943 title "Instantaneous Frequency of a Signal" @default.
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- W1569684943 doi "https://doi.org/10.1002/9780470611203.ch2" @default.
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