Three algorithms to estimate instantaneous frequency of a frequency-modulated signal is discussed. These algorithms are 7 based on Hilbert transform, Haar wavelet, and generalized pencil of function (GPOF) methods. While GPOF-based frequency detection method appears to be least sensitive to noise, wavelet-based method is easiest to implement. The latter method is 9 also computationally more e c...

Hilbert-Huang Transform (HHT) is a novel data analysis technique for nonlinear and non-stationary data. We present a time-frequency analysis of both simulated light curves and an X-ray burst from the X-ray burster 4U 1702-429 with both the HHT and the Windowed Fast Fourier Transform (WFFT) methods. Our results show that the HHT method has failed in all cases for light curves with Poissonian flu...

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.

Model selection is one of the most important tasks in the identification of blackbox systems. In this paper, we give a novel model selection method from the viewpoint of functional analysis. We formulate the system identification problem as a function approximation problem in a reproducing kernel Hilbert space (RKHS), where the approximation error is measured by the RKHS norm. Within this frame...

There is one concept in medicine which is prominent, the symptom. The omnipresence of the symptom seems, however, not to be reflected by an equally prominent curiosity aimed at investigating this concept as a phenomenon. In classic, traditional or conventional medical diagnostics and treatment, the lack of distinction with respect to the symptom represents a minor problem. Faced with enigmatic ...

most geologic changes have a seismic response but sometimes this is expressed only in certain spectral ranges hidden within the broadband data. spectral decomposition is one of the methods which can be utilized to help interpreting such cases. there are several time-frequency methods including: short-time fourier transform (stft), continuous wavelet transform (cwt), wigner-ville distribution (w...

Signals in a two-channel quadrature mirror filter bank are decomposed into low and high frequency components. Similarly, analytic signals can be extracted from the original signal with only positive or negative frequency contents. Multirate systems based on this idea are called quadrature mirror Hilbert transformers. Just like the case of quadrature mirror filter banks, the FIR and IIR designs ...

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...