The Hilbert-based time-frequency analysis has promising capacity to reveal the time-variant behaviors of a system. To admit well-behaved Hilbert transforms, component decomposition of signals must be performed beforehand. This was first systematically implemented by the empirical mode decomposition (EMD) in the Hilbert-Huang transform, which can provide a time-frequency representation of the si...

The parameters in a nuclear magnetic resonance (NMR) free induction decay (FID) signal contain information that is useful in magnetic field measurement, magnetic resonance sounding (MRS) and other related applications. A real time sampled FID signal is well modeled as a finite mixture of exponential sequences plus noise. We propose to use the Hilbert-Huang Transform (HHT) for noise reduction an...

In this paper, by using the sequence of adjointable operators from pro-C*-algebra $ mathcal{A} $ into a Hilbert $ mathcal{A} $-module $ E $. We introduce frames with bounds in pro-C*-algebra $ mathcal{A} $. New frames in Hilbert modules over pro-C*-algebras are called standard $ ast $-frames of multipliers. Meanwhile, we study several useful properties of standard $ ast $-frames in Hilbert modu...

-A new method is presented for the texture analysis and segmentation of seismic images. The texture of a seismic image is described in terms either of seismic horizons' features (e.g. length, reflection strength, geometrical appearance), or in terms of Hilbert transform features (magnitude, phase, instantaneous frequency) or in terms of features related to the generalized runs. Seismic image se...

We propose a new band-extrapolation method using an iterative Hilbert-transform procedure, which is applicable for band-limited complex-frequency data obtained from a Fourier-transform phase-modulation fluorometer (FT-PMF). Without the band limitation, the real and the imaginary parts of the complex-frequency data obtained from the FT-PMF form a Hilbert-transform pair because of causality. Howe...