Abstract
The concept of Instantaneous Frequency is still not clearly defined. Current operational definitions give rise to physical paradoxes, difficulting proper interpretation of the obtained results. In this paper, we discuss why those paradoxes appear, and show how they can be avoided. We introduce a new definition of Instantaneous Frequency, which yields physically consistent results. This is confirmed with the help of several examples.

Abstract
It has often been reported and is now well established that the traditional definition of Instantaneous Frequency (IFt) fails in the presence of multicomponent signals. New definitions of IFt have recently been proposed, in an attempt to cope with the difficulties of the traditional one. In this paper, we will address the reasons for failure of the traditional definition, show that it can also fail with monocomponent signals, and show how its behaviour can be predicted for any type of signal, thus generalizaing previous results. We will also analyse the performance in noise of one of the recently proposed definitions of IFt.

Abstract
A subspace-based on-line identification algorithm based on one specific technique, based on Van Overschee and De Moor's results, but can be adapted to other similar methods since they all recover from the state sequence and the observability matrix is presented. These results relate an estimated Kalman filter sequence with an oblique projection. With further improvements, the algorithm can adapt to the identification of time-variant systems.

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