The Hilbert-Huang transform (HHT) is a powerful method for nonlinear and non-stationary vibrations analysis. This approach consists of two basic parts of empirical mode decomposition (EMD) and Hilbert spectral analysis (HSA). To achieve the reliable results, Bedrosian and Nuttall theorems should be satisfied. Otherwise, the phase and amplitude functions are mixed together and consequently, the ...

The p-norm of the Hilbert transform is the same as the p-norm of its truncation to any Lebesgue measurable set with strictly positive measure. This fact follows from two symmetry properties, the joint presence of which is essentially unique to the Hilbert transform. Our result applies, in particular, to the finite Hilbert transform taken over ( — 1,1), and to the one-sided Hilbert transform tak...

In this paper, those splendid characters of the Hilbert transform let the processes that taking wavelet transform after taking Hilbert transform for the statistic self-similarity processes FBM [ ) (t BH ] become another processes, that firstly taking Hilbert transform for the wavelet function ) (t φ and forming a new wavelet function ) (t ψ , secondly taking the wavelet transform for ) (t BH . ...

Abstract This paper presents a general expression for a number-theoretic Hilbert transform (NHT). The transformations preserve the circulant nature of the discrete Hilbert transform (DHT) matrix together with alternating values in each row being zero and non-zero. Specific examples for 4point, 6-point, and 8-point NHT are provided. The NHT transformation can be used as a primitive to create cry...

The Hilbert transform is essentially the only singular operator in dimension 1. This undoubtedly makes it one of the the most important linear operators in harmonic analysis. The Hilbert transform has had a profound bearing on several theoretical and physical problems across a wide range of disciplines; this includes problems in Fourier convergence, complex analysis, potential theory, modulatio...

In joint work with C. Thiele, the author has shown that A. Calderón’s bilinear Hilbert transform extends to a bounded operator on certain products of L spaces. This article illustrates the method of proof by giving a complete proof of an inequality which is slightly weaker than the original conjecture of Calderón concerning this transform. 1991 Mathematics Subject Classification: 42A50

Abstract: This paper presents several experimental findings related to the basic discrete Hilbert transform. The errors in the use of a finite set of the transform values have been tabulated for the more commonly used functions. The error can be quite small and, for example, it is of the order of 10 for the chirp signal. The use of the discrete Hilbert transform in hiding information is presented.