There are many methods able to extract the instantaneous frequencies from a time series for practical applications. Gabor’s method is one of the most popular and simple methods. For wide band time series, Gabor’s method may produce negative frequencies. The limitation of Gabor’s method is that, in order to avoid resulting with negative frequencies, it can only be applied to time series with mon...

This paper proposes a general framework to interpret the concept of Instantaneous Frequency (IF) in three-phase systems. The first recalls conventional frequency-domain analysis based on Fourier transform as well definition IF which is analytic signals. link between signals and Clarke voltages an ac power system also shown. Then well-known five paradoxes are stated. In second part paper, approa...

The time-varying microstructure of sleep EEG spindles may have clinical significance in dementia studies and can be quantified with a number of techniques. In this paper, the sleep spindle is modeled as an AM-FM signal in terms of six parameters, three quantifying the instantaneous envelope (IE) and three quantifying the instantaneous frequency (IF) of the spindle model. An application of such ...

Properties determining optimal behavior of continuous analytic wavelet functions are investigated, and wavelet functions nearly obtaining such behavior are identified. This is accomplished through detailed investigation of the generalized Morse wavelets, a highly flexible family of exactly analytic continuous wavelets. The degree of time/frequency localization, the existence of a unique interpr...

Abstract Recently, the synchrosqueezing transform (SST) was developed as an alternative to the empirical mode decomposition scheme to separate a non-stationary signal with time-varying amplitudes and instantaneous frequencies (IFs) into a superposition of frequency components that each have well-defined IFs. The continuous wavelet transform (CWT)-based SST sharpens the time-frequency representa...