The Synchrosqueezing transform is a time-frequency analysis method that can decompose complex signals into time-varying oscillatory components. It is a form of time-frequency reassignment that is both sparse and invertible, allowing for the recovery of the signal. This article presents an overview of the theory and stability properties of Synchrosqueezing, as well as applications of the techniq...

The analysis of historical or ethnical musical instruments can provide means to verify and broaden our knowledge on musical acoustics. The Turkish tanbur, a member of evidently the oldest group of lute instruments, is a good example. Some important features of the instrument include its body resonator (a wooden hemispherical shell covered with a shallow plate) without a sound hole, its violin-l...

Future design procedures for civil structures, especially those to be protected from extreme and blast related loads, will need to account for temporal evolution of their frequency content. Separate time analysis and frequency analysis by themselves do not fully describe the nature of these nonstationary dynamic loads. In the past few years, significant effort has been devoted to wavelets and t...

We develop a theory of almost periodic elements in Banach algebras and present an abstract version of a noncommutative Wiener’s Lemma. The theory can be used, for example, to derive some of the recently obtained results in time-frequency analysis such as the spectral properties of the finite linear combinations of time-frequency shifts.

The effects of hypertension are chronic and continuous; it affects gait, balance, and fall risk. Therefore, it is desirable to assess gait health across hypertensive and nonhypertensive subjects in order to prevent or reduce the risk of falls. Analysis of electromyography (EMG) signals can identify age related changes of neuromuscular activation due to various neuropathies and myopathies, but i...

In this work, a class of multivariate multiwavelet packages with multi-scale are introduced, which are generalizations of multivariant wavelet packages. A method for designing a sort of biorthogonal multiwavelet packages in higher dimensions is presented and their biorthogonality property is characterized by virtue of time-frequency analysis method, matrix theory, and operator theory. Three bio...

Gaussian signals play a very special role in classical time-frequency analysis because they are solutions of apparently unrelated problems such as minimum uncertainty or positivity and separability of Wigner-Ville distributions. We investigate here some of the logical connections which exist between these diierent features, and we discuss some examples and counterexamples of their extension to ...

We generalize the classical coorbit space theory developed by Feichtinger and Gröchenig to quasi-Banach spaces. As a main result we provide atomic decompositions for coorbit spaces defined with respect to quasi-Banach spaces. These atomic decompositions are used to prove fast convergence rates of best n-term approximation schemes. We apply the abstract theory to time-frequency analysis of modul...

In time-frequency analysis there are four bilinear domains commonly used: time-frequency, ambiguity, temporal auto-correlation, and spectral auto-correlation. This paper introduces four new domains that are quadralinear in the signal. These four domains are each a function of three of the four variables used in the bilinear domains. Properties of these quantities are developed and an applicatio...

In this paper we present a comparison of Neural Network Training Algorithms for obtaining a Time Frequency Distribution (TFD) of a signal whose frequency components vary with time. The method employs various algorithms used in NNs which are trained by using the spectrograms of several training signals as input and TFDs that are highly concentrated along the instantaneous frequencies (IFs) of th...