many of nonlinear systems in the field of engineering such as nano-resonator and atomic force microscope can be modeled based on duffing equation. analytical frequency response of this system helps us analyze different interesting nonlinear behaviors appearing in its response due to its rich dynamics. in this paper, the general form of duffing equation with cubic nonlinearity as well as paramet...

We present the application of a novel method of time-series analysis, the Hilbert-Huang Transform, to the search for gravitational waves. This algorithm is adaptive and does not impose a basis set on the data, and thus the time-frequency decomposition it provides is not limited by time-frequency uncertainty spreading. Because of its high time-frequency resolution it has important applications t...

spectral decomposition of time series has a significant role in seismic data processing and interpretation. since the earth acts as a low-pass filter, it changes frequency content of passing seismic waves. conventional representing methods of signals in time domain and frequency domain cannot show time and frequency information simultaneously. time-frequency transforms upgraded spectral decompo...

For a bounded linear operator on Hilbert space we define a sequence of the so-called weakly extremal vectors‎. ‎We study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors‎. ‎Also we show that any quasinilpotent operator $T$ has an hypernoncyclic vector‎, ‎and so $T$ has a nontrivial hyperinvariant subspace‎.

The Hilbert and Fourier transforms are tools used for signal analysis in the time/frequency domains. The Hilbert transform is applied to casual continuous signals. The majority of the practical signals are discrete signals and they are limited in time. It appeared therefore the need to create numeric algorithms for the Hilbert transform. Such an algorithm is a numeric operator, named the Discre...

We present the application of a novel method of time-series analysis, the Hilbert-Huang Transform, to the search for gravitational waves. This algorithm is adaptive and does not impose a basis set on the data, and thus the time-frequency decomposition it provides is not limited by time-frequency uncertainty spreading. Because of its high time-frequency resolution it has important applications t...

Hilbert Vibration Decomposition (HVD) is introduced to the voltage flicker analysis. When voltage flicker accompanies with high order harmonics, the instantaneous frequency of its analytic signal in principle consists of two different parts, power frequency and a rapidly varying asymmetrical oscillating part. The important property of the instantaneous frequency offers a direct way to estimate ...

The Hilbert-Huang-Transform (HHT) has proven to be an appropriate multiscale analysis technique specifically for nonlinear and nonstationary time series on non-equidistant grids. It is empirically adapted to the data: first, an additive decomposition of the data (empirical mode decomposition, EMD) into certain multiscale components is computed, denoted as intrinsic mode functions. Second, to ea...