Abstract
The improvement of the readability of time-frequency transforms is an important topic in the field of fast-oscillating signal processing. The reassignment method is often used due to its adaptivity to different transforms and nice formal properties. However, it strongly depends on the selection of the analysis window and it requires the computation of the same transform using three different but well-defined windows. The aim of this work is to provide a simple method for spectrogram reassignment, named FIRST (Fast Iterative and Robust Reassignment Thinning), with comparable or better precision than classical reassignment method, a reduced computational effort, and a near independence of the adopted analysis window. To this aim, the time-frequency evolution of a multicomponent signal is formally provided and, based on this law, only a subset of time-frequency points is used to improve spectrogram readability. Those points are the ones less influenced by interfering components. Preliminary results show that the proposed method can efficiently reassign spectrograms more accurately than the classical method in the case of interfering signal components, with a significant gain in terms of required computational effort.
Highlights
A sparse representation of a function strongly depends on its properties
The proposed iterative reassignment method has been tested on several synthetic signals with more than one component and different instantaneous frequencies functions
The results have been directly compared with the standard reassignment method to appreciate and evaluate the step forward provided by the proposed method in terms of improved spectrogram readability and computational gain
Summary
A sparse representation of a function strongly depends on its properties This task is made more difficult in the case of non-stationary time-frequency functions [1,2,3,4], as a single linear transform is not able to provide a really sparse representation of the function. K =1 where f k is the k-th mode, ak and φk respectively are its amplitude and phase functions of the time variable t while M is the number of modes. The main goal is to estimate the instantaneous frequency (IF) of each mode, i.e., the positive value of the derivative with respect to the time variable of the phase φk (t) [5,6,7]. It is desirable to Mathematics 2019, 7, 358; doi:10.3390/math7040358 www.mdpi.com/journal/mathematics
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