Signal characterization using generalized "Time-phase derivatives" representation

Natural signals are often characterized by a complex timefrequency behaviour. These signals exist in many different applications and systems from underwater acoustic to audio signals with sound attacks or electrical systems with partial discharges and commutation switches, for example. There is a huge number of Time-Frequency (TF) methods that aim to characterize these signals in terms of first phase derivative analysis (i.e Instantaneous Frequency Law). Recently, we introduced the time frequency distribution based on complex lag arguments. This distribution is able to reduce inner interferences terms which appear when studying non-linear TF components. It also offers access to an instantaneous law representation of any phase derivative order. In this paper, we use these two properties to study highly non-stationary signals as well as transient signals.