Abstract
Ville's definition of Instantaneous Frequency (IF), even though widely used and accepted, fails in most cases of practical interest. This failure has been often reported, namely in the multicomponent case. In this paper, we will analyze the advantages and shortcomings of that definition, and determine when and why it fails, integrating all previously reported cases of failure in a simple unified theory. We will also be able to extrapolate and predict the behavior of the traditional definition for any type of multicomponent signal. Alternative definitions of IF are discussed.

Abstract
The concepts of Instantaneous Frequency (IFt) and Instantaneous Bandwidth (IBt) have traditionally been considered as independent spectral features. Recent work has suggested, however, that the spectral dynamics of the signal (and, hence, its IFt) may have an impact on IBt and on the achievable spectral resolution. In this article, we consider model based AR spectral estimators. Simulations are done with several distinct time-frequency tools, to confirm the theoretical predictions.

Abstract

Abstract
This paper examines a modified version of the instantaneous power spectrum (IPS). The short duration periodogram and the pseudo Wigner–Ville distribution (PWD) have been used extensively to display the time-varying spectral information. Disadvantages of the periodogram are its inherently poor resolution due to the requirement of matching the resolution width to the spectral dynamics of the signal. Potential problems associated with PWD are spectral cross terms and an inability to resolve spectral components at the endpoints of the analysis segment. A modified version of IPS is shown to be less sensitive to these types of problems. In addition, IPS can work with real valued signals sampled at the traditional Nyquist rate. © 1990 IEEE

Abstract

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.