Short communication: on the uniqueness of the definition of the amplitude and phase of the analytic signal

Authors:
Stefan L. Hahn
Affiliations:
Institute of Radioelectronics, Warsaw University of Technology, Nowowiejska 15/19, 00-665 Warsaw, Poland
Venue:
Signal Processing - Special section: Hans Wilhelm Schüßler celebrates his 75th birthday
Year:
2003

Citing 3
Cited 1

On an ambiguity in the definition of the amplitude and phase of a signal

Signal Processing
On the analytic signal, the Teager-Kaiser energy algorithm, andother methods for defining amplitude and frequency

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Modified Cohen-Lee time-frequency distributions and instantaneousbandwidth of multicomponent signals

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Estimation of the instantaneous amplitude and the instantaneous frequency of audio signals using complex wavelets

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Abstract

In 1999 three prominent scientists suggested in a paper printed in this journal that the definitions of the instantaneous amplitude, phase and frequency of an analytic signal are ambiguous. However, a detailed analysis using the notion of instantaneous complex frequency and Mikusinski's theory of distributions shows that the above definitions are unique. Several aspects of this problem are discussed. The approach using moments defined using the Wigner distribution confirms the above-mentioned uniqueness.