Related papers: Theory of the Hilbert Spectrum
In this paper we present the latent signal analysis problem as a recasting of the complex extension problem. Almost universally, the approach has been to use the Hilbert Transform (HT) to construct Gabor's analytic signal. This approach…
The ideas of instantaneous amplitude and phase are well understood for signals with real-valued samples, based on the analytic signal which is a complex signal with one-sided Fourier transform. We extend these ideas to signals with…
This text describes a generalization of the analytic signal (Gabor, 1946) approach for the definition of instantaneous amplitude and phase to the case of multivariate signals. It was originally written as an appendix for another paper,…
The nonstationary nature of signals and nonlinear systems require the time-frequency representation. In time-domain signal, frequency information is derived from the phase of the Gabor's analytic signal which is practically obtained by the…
Based on a unique waveform with strong exponential localization property, an exact mathematical method for solving problems in signal analysis in time-frequency domain is presented. An analogue of the Gabor frame exposes the non-commutative…
The analysis of the time-frequency content of a signal is a classical problem in signal processing, with a broad number of applications in real life. Many different approaches have been developed over the decades, which provide alternative…
We propose a new approach for studying the notion of the instantaneous frequency of a signal. We build on ideas from the Synchrosqueezing theory of Daubechies, Lu and Wu and consider a variant of Synchrosqueezing, based on the short-time…
Time-frequency representations such as the spectrogram are commonly used to analyze signals having a time-varying distribution of spectral energy, but the spectrogram is constrained by an unfortunate tradeoff between resolution in time and…
Computation of the instantaneous phase and amplitude via the Hilbert Transform is a powerful tool of data analysis. This approach finds many applications in various science and engineering branches but is not proper for causal estimation…
Gabor transform is one of the performed tools for time-frequency signal analysis. The principal aim of this paper is to generalize the Gabor Fourier transform to the quaternion linear canonical transform. Actually, this transform gives us…
The very old problem of extracting frequencies from time signals is addressed in the case of signals that are very short as compared to their intrinsic time scales. The solution of the problem is not only important to the classic signal…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
In this paper, the instantaneous frequency estimation of nonstationary signals is considered. The instantaneous frequency is estimated from the timefrequency representation where certain percent of the coefficients is missing. The…
Gravitational wave astronomy relies on the use of multiple detectors, so that coincident detections may distinguish real signals from instrumental artifacts, and also so that relative timing of signals can provide the sky position of…
An exact and general expression for the analytic wavelet transform of a real-valued signal is constructed, resolving the time-dependent effects of non-negligible amplitude and frequency modulation. The analytic signal is first locally…
The generalizations of instantaneous frequency and instantaneous bandwidth to a bivariate signal are derived. These are uniquely defined whether the signal is represented as a pair of real-valued signals, or as one analytic and one…
New definitions are suggested for frequencies which may be instantaneous or not. The Heisenberg-Gabor inequality and the Shannon sampling theorem are briefly discussed.
The hyperanalytic signal is the straight forward generalization of the classical analytic signal. It is defined by a complexification of two canonical complex signals, which can be considered as an inverse operation of the Cayley-Dickson…
In the tradition of Gabor's 1946 landmark paper [1], we advocate a time-frequency (TF) approach to communications. TF methods for communications have been proposed very early (see the box History). While several tutorial papers and book…
We propose a general quantum theory of optical phase and instantaneous frequency in the time domain for slowly varying optical signals. Guided by classical estimation theory, we design homodyne phase-locked loops that enable quantum-limited…