Necessary and sufficient conditions are presented for a positive measure to be the spectral measure of a half-line Schrödinger operator with square integrable potential.

A new enhanced Itakura (E-Itakura) speech distortion measure is proposed in this paper. It incorporates masking properties of the human auditory system into the original Itakura measure. Inaudible noise components masked by speech signals are excluded from the calculation of the E-Itakura measure, while the intrinsic advantage of the Itakura measure is retained. The proposed new measure has bee...

We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation method and obtain compact expressions for the covariance. We illustrate the universality of this measure by presenting the spectral analysis of the quantum kic...

In this paper performance limits of optical OFDM transmission systems are investigated. The maximum achievable spectral efficiency is limited by additive noise of optical amplifiers and non-linear fiber effects. In order to assess this measure, a “weakly nonlinear” system model is used. For a given transmission scenario, there is a minimum power of signal distortion at a specific optical launch...

Vector-valued, asymptotically stationary stochastic processes on r-compact locally compact abelian groups are studied. For such processes, we introduce a stationary spectral measure and show that it is discrete if and only if the asymptotically stationary covariance function is almost periodic. Using an “almost periodic Fourier transform” we recover the discrete part of the spectral measure and...

We examine the application of spectral clustering for breaking up the behaviour of a multi-agent system in space and time into smaller, independent elements. We extend the clustering into the temporal domain and propose a novel similarity measure, which is shown to possess desirable temporal properties when clustering multi-agent behaviour. We also propose a technique to add knowledge about eve...

Kernel selection is a fundamental problem of kernel methods. Existing measures for kernel selection either provide less theoretical guarantee or have high computational complexity. In this paper, we propose a novel kernel selection criterion based on a newly defined spectral measure of a kernel matrix, with sound theoretical foundation and high computational efficiency. We first show that the s...

We revisit the concept of spectral averaging and point out its origin in connection with one-parameter subgroups of SL2(R) and the corresponding Möbius transformations. In particular, we identify exponential Herglotz representations as the basic ingredient for the absolute continuity of average spectral measures with respect to Lebesgue measure and the associated spectral shift function as the ...

A method for efficient quantization of speech spectral models is proposed. The impulse response of the model is coded in two spectral subbands of unequal width. The distortion measure used is a squared error between impulse responses. The quality obtained at 22 bits per frame is as good as that of Split Vector Quantization of Line Spectral Frequencies at 24 bits per frame.

There is evidence that the mechanisms leading to epileptic seizures can be understood by continuously tracking the ongoing spatio-temporal mappings in the brain. We propose to quantify the spatio-temporal dynamics by using a SOM-based Similarity Index (SI) measure. While it is shown that this measure is statistically as accurate as the original SI measure, it is also computationally faster and ...