Abstract Space-time and time-varying metastructures have attracted a lot of research interest in recent years. On the other hand, digital programmable metasurfaces also gained great attention owing to their powerful capabilities controlling electromagnetic (EM) fields waves real time, which is very suitable for implementing spatiotemporal modulations manner. Accordingly, space-time-coding (STC)...

Time series are an important data class that includes recordings ranging from radio emissions, seismic activity, global positioning data, and stock prices to EEG measurements, vital signs, and voice recordings. Rapid growth in sensor and recording technologies is increasing the production of time series data and the importance of rapid, accurate analyses. Time series data are commonly analyzed ...

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...

In time-frequency analysis Hilbert transformation is used to define analytic signals based on which meaningful instantaneous amplitude and instantaneous frequency are defined. In relation to this background we study characteristic properties of the real-valued measurable functions ρ(t) and θ(t), t ∈ R, such that H(ρ(·) cos θ(·))(t) = ρ(t) sin θ(t), ρ(t) ≥ 0, where H is the Hilbert transformatio...

Compactly supported wavelet bases for Sobolev spaces is investigated. Steming from a pair of compactly supported refinale functions with multiscale dilation factor in space 2 3 ( ) L R meeting a very mild condition, we provide a general approach for constructing wavelet bases, which is the generalization of univariate wavelets in Hilbert space. The notion of orthogonal non-tensor product trivar...

In order to distinguish the difference of non-stationary signals, the novel time-frequency analysis approach, i.e. Hilbert-Huang transform (HHT), is applied in this paper. Firstly, Hilbert-Huang transform is briefly introduced. Secondly, two different non-stationary signals are described in Empirical Mode Decomposition (EMD) and Hilbert spectra. With these results, the two signals that looked a...