The improvement in the temporal resolution of seismic data is a critical issue in hydrocarbon exploration. It is important for obtaining more detailed structural and stratigraphic information. Many methods have been introduced to improve the vertical resolution of reflection seismic data. Each method has advantages and disadvantages which are due to the assumptions and theories governing their ...

Fundamental to the theory of joint signal representations is the idea of associating a variable, such as time or frequency, with an operator, a concept borrowed from quantum mechanics. Each variable can be associated with a Hermitian operator, or equivalently and consistently, as we show, with a parame-terized unitary operator. It is well-known that the eigenfunctions of the unitary operator de...

a r t i c l e i n f o a b s t r a c t Keywords: Time–frequency analysis Windowed Fourier transform Wavelet transform Synchrosqueezing Time–frequency representations (TFRs) of signals, such as the windowed Fourier transform (WFT), wavelet transform (WT) and their synchrosqueezed versions (SWFT, SWT), provide powerful analysis tools. Here we present a thorough review of these TFRs, summarizing al...

Signal processing is an important issue that should be considered prior to recording mechanomyographic (MMG) signals. The first studies in this area found that the fast Fourier transform and maximum entropy spectrum estimation techniques provided MMG frequency spectra that were very similar in shape. The shape of the spectrum from the maximum entropy spectrum estimation technique, however, was ...

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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...

By use of window functions, time-frequency analysis tools like Short Time Fourier Transform overcome a shortcoming of the Fourier Transform and enable us to study the timefrequency characteristics of signals which exhibit transient oscillatory behavior. Since the resulting representations depend on the choice of the window functions, it is important to know how they influence the analyses. One ...

The notions of time, frequency, and scale are generalized using concepts from unitary operator theory and applied to time-frequency analysis, in particular the wavelet and short-time Fourier transform orthonormal bases and Cohen's class of bi-linear time-frequency distributions. The result is an infinite number of new signal analysis and processing tools that are implemented simply by prewarpin...