Krylov subspace spectral (KSS) methods have been demonstrated to be effective tools for solving time-dependent variable-coefficient PDE. They employ techniques developed by Golub and Meurant for computing elements of functions of matrices to approximate each Fourier coefficient of the solution using a Gaussian quadrature rule that is tailored to that coefficient. In this paper, we apply this sa...

On the wavelet-packet modulation scheme, wavelet packets are used as carriers, where information to be transmitted is encoded, via an inverse wavelet packet transform, as the coefficient of wavelet packets. The power spectrum density (PSD) of the modulated signals describes the property of modulation in frequency domain, which is discussed by many researchers by simulation. In this paper, the f...

Krylov subspace spectral (KSS) methods have been demonstrated to be effective tools for solving time-dependent variable-coefficient PDE. They employ techniques developed by Golub and Meurant for computing elements of functions of matrices to approximate each Fourier coefficient of the solution using a Gaussian quadrature rule that is tailored to that coefficient. In this paper, we apply this sa...

The spectral decomposition of normal linear (bounded) operators and the polar decomposition of arbitrary linear (bounded) operators on Hilbert spaces have been interesting and technically useful results in operator theory [3, 9, 13, 20]. The development of the concept of von Neumann algebras on Hilbert spaces has shown that both these decompositions are always possible inside of the appropriate...

Spectral CT is a promising new imaging modality that is able to provide spectral information of several pre-selected energy ranges in one image acquisition, which allows quantitative decomposition of multiple materials. In addition to conventional reconstruction, novel decomposition techniques should be developed to realize material separation. Decomposition of multienergy X-ray data into basis...

The spectral methods seek the numerical solutions by a set of known polynomials. The main advantage of using spectral methods for solving atmospheric problems is the high efficiency and conservations of important quadratic quantities such as kinetic energy and enstrophy. Namely, we can get very high accuracy through the exponential convergence. The conservation of the quadratic quantities are i...

Material composition can be estimated from spectral information acquired using photon counting x-ray detectors with pulse height analysis. Non-ideal effects in photon counting x-ray detectors such as charge-sharing, k-escape, and pulse-pileup distort the detected spectrum, which can cause material decomposition errors. This work compared the performance of two empirical decomposition methods: a...

Two fundamental aspects of frequency analysis shape the functional organization of primary auditory cortex. For one, the decomposition of complex sounds into different frequency components is reflected in the tonotopic organization of auditory cortical fields. Second, recent findings suggest that this decomposition is carried out in parallel for a wide range of frequency resolutions by neurons ...