Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Time-frequency analysis: theory and applications
Time-frequency analysis: theory and applications
ICASSP '97 Proceedings of the 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '97) -Volume 1 - Volume 1
Time-frequency distributions with complex argument
IEEE Transactions on Signal Processing
Generalized Representation of Phase Derivatives for Regular Signals
IEEE Transactions on Signal Processing
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The detection and localization of transient signals is nowadays a typical point of interest when we consider the multitude of existing transient sources, such as electrical and mechanical systems, underwater environments, audio domain, seismic data, and so forth. In such fields, transients carry out a lot of information. They can correspond to a large amount of phenomena issued from the studied problem and important to analyze (anomalies and perturbations, natural sources, environmental singularities, ...). They usually occur randomly as brief and sudden signals, such as partial discharges in electrical cables and transformers tanks. Therefore, motivated by advanced and accurate analysis, efficient tools of transients detection and localization are of great utility. Higher order statistics, wavelets and spectrogram distributions are well known methods which proved their efficiency to detect and localize transients independently to one another. However, in the case of a signal composed by several transients physically related and with important energy gap between them, the tools previously mentioned could not detect efficiently all the transients of the whole signal. Recently, the generalized complex time distribution concept has been introduced. This distribution offers access to highly concentrated representation of any phase derivative order of a signal. In this paper, we use this improved phase analysis tool to define a new concept to detect and localize dependant transients taking regard to the phase break they cause and not their amplitude. ROC curves are calculated to analyze and compare the performances of the proposed methods.