An improved AM-FM decomposition method for computing the instantaneous frequency of non-stationary signals

Band-limited functions, and Time-Frequency Analysis of Non-Stationary Signals: Application to Bioelectrical Signals Analysis

“…In this way, the obtention of HSA outputs is straightforward: approximate Hilbert conjugates, analytic functions, local energies, and instantaneous phase and frequency functions are obtained directly with relatively ease and little computational effort, requiring only the Fourier Analysis and the evaluation of explicit formulae. This is a remarkable fact, since in the HSA general framework, the computation of the instantaneous frequency is not straightforward and demand computational efforts, subject to time consuming procedures and numerical errors ( [15], [13], [52], [53], [128], [124], [35], [113]).…”

“…The case of crossover frequencies has been extensively discussed in recent decades [72]. Furthermore, among other technical problems to overcome, the mathematical analysis of the so-called sifting process in EMD, as a data-driven technique, is very challenging, and most of its success comes from practice (see [13], [132], [101], [53], [137], [49], [128], [32], [51], [37], [47]).…”

On the Concept of Frequency in Signals Processing: A discussion

“…Furthermore, the mathematical foundation of all these data-driven techniques (specially the so-called sifting process in EMD) turn to be very challenging, and most of the confidence they generate comes from numerical experiments and particular data analyses. There are also technical problems to overcome (see [5], [70], [55], [49], [37], [76], [34], [68], [24], [38], [28], [33] for theory and applications).…”