The time–frequency (TF) analysis is an effective tool in seismic signal processing. The
sparsity-based TF transforms have been widely used to obtain high localized TF …

We review the quaternionic Fourier transform (QFT). Using the properties of the QFT we
establish an uncertainty principle for the right-sided QFT. This uncertainty principle …

Some signals captured in practical applications are usually composed of a series of modes
that have multivalued time-dependent instantaneous frequency (IF), ie, transient signal …

We generalize the linear canonical transform (LCT) to quaternion‐valued signals, known as
the quaternionic linear canonical transform (QLCT). Using the properties of the LCT we …

Linear canonical transforms (LCTs) are a family of integral transforms with wide application
in optical, acoustical, electromagnetic, and other wave propagation problems. The Fourier …

Inspired by a definition of the closed-form instantaneous cross-correlation Wigner
distribution (Zhang, 2019), we generalize the notion of Wigner distribution to the so-called …

Thin interbeds, which are made of several thin layers, are critical geological structures in
seismic exploration. Due to the limited seismic resolution, thin interbeds cannot be easily …

In the present paper, we generalize the linear canonical transform (LCT) to quaternion‐
valued signals, known as the quaternionic LCT (QLCT). Using the properties of the LCT, we …

To tackle a challenge in high-dimensional complex features information processing, this
study extends the permanent scale Wigner distribution and the single scale-Wigner …

The classical uncertainty principle plays an important role in quantum mechanics, signal
processing and applied mathematics. With the development of novel signal processing …