Hilbert transform (HT) is an important tool in constructing analytic signals for various purposes, such as envelope and instantaneous frequency analysis, amplitude modulation, shift invariant wavelet analysis and Hilbert-Huang decomposition. In this work we introduce a method for computation of HT based on the discrete cosine transform (DCT). We show that the Hilbert transformed signal can be o...

The analytic signal method via the Hilbert transform is a key tool in signal analysis and processing, especially in the time-frquency analysis. Imaging and other applications to multidimensional signals call for extension of the method to higher dimensions. We justify the usage of partial Hilbert transforms to define multidimensional analytic signals from both engineering and mathematical persp...

In this paper we decompose the Hilbert Spectrum of an audio mixture into a number of subspaces to segregate the sources. Empirical mode decomposition (EMD) together with Hilbert transform produces Hilbert spectrum (HS), which is a fineresolution time-frequency representation of a non-stationary signal. EMD decomposes the mixture signal into some intrinsic oscillatory modes called intrinsic mode...

Frames which can be generated by the action of some operators (e.g. translation, dilation, modulation, ...) on a single element $f$ in a Hilbert space, called coherent frames. In this paper, we introduce a class of continuous frames in a Hilbert space $mathcal{H}$ which is indexed by some locally compact group $G$, equipped with its left Haar measure. These frames are obtained as the orbits of ...

The concept of empirical mode decomposition (EMD) and the Hilbert spectrum (HS) has been developed rapidly in many disciplines of science and engineering since Huang et al. (1998) invented EMD. The key feature of EMD is to decompose a signal into so-called intrinsic mode function (IMF). Furthermore, the Hilbert spectral analysis of intrinsic mode functions provides frequency information evolvin...

Almost all variables in biology are nonstationarily stochastic. For these variables, the conventional tools leave us a feeling that some valuable information is thrown away and that a complex phenomenon is presented imprecisely. Here, we apply recent advances initially made in the study of ocean waves to study the blood pressure waves in the lung. We note first that, in a long wave train, the h...