Complex spectral analysis and test function spaces

We consider complex eigenstates of unstable Hamiltonian and its physically meaningful regions. Starting from a simple model of a discrete state interacting with a continuum via a general potential, we show that its Lippmann-Schwinger solution set can be decomposed into a free-field set, a set containing lower half plane pole of Green's function and a set containing upper half pole of Green's function. From here distinctive complex eigenstates corresponding to each pole are constructed. We note that on the real line square integrable functions can be decomposed into Hardy class above and below functions which behave well in their respective complex half planes. Test function restriction formulas which remove unphysical growth are given. As a specific example we consider Friedrichs model which solutions and complex eigenstates are known, and compare numerically calculated total time evolution with test function restricted complex eigenstates for various cases. The results shows that test function restricted complex eigenstates capture the essence of decay phenomena quite well.Comment: 32 page

Testing temporal constancy of the spectral structure of a time series

Statistical inference for stochastic processes with time-varying spectral characteristics has received considerable attention in recent decades. We develop a nonparametric test for stationarity against the alternative of a smoothly time-varying spectral structure. The test is based on a comparison between the sample spectral density calculated locally on a moving window of data and a global spectral density estimator based on the whole stretch of observations. Asymptotic properties of the nonparametric estimators involved and of the test statistic under the null hypothesis of stationarity are derived. Power properties under the alternative of a time-varying spectral structure are discussed and the behavior of the test for fixed alternatives belonging to the locally stationary processes class is investigated.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ179 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

The correction for spectral mismatch effects on the calibration of a solar cell when using a solar simulator

A general expression was derived to enable calculation of the calibration error. The information required includes the relative spectral response of the reference cell, the relative spectral response of the cell under test, and the relative spectral irradiance of the simulator (over the spectral range defined by cell response). The spectral irradiance of the solar AMX is assumed to be known

The quantile spectral density and comparison based tests for nonlinear time series

In this paper we consider tests for nonlinear time series, which are motivated by the notion of serial dependence. The proposed tests are based on comparisons with the quantile spectral density, which can be considered as a quantile version of the usual spectral density function. The quantile spectral density 'measures' sequential dependence structure of a time series, and is well defined under relatively weak mixing conditions. We propose an estimator for the quantile spectral density and derive its asympototic sampling properties. We use the quantile spectral density to construct a goodness of fit test for time series and explain how this test can also be used for comparing the sequential dependence structure of two time series. The method is illustrated with simulations and some real data examples

Forest Species Identification with High Spectral Resolution Data

Data collected over the Sleeping Bear Sand Dunes Test Site and the Saginaw Forest Test Site (Michigan) with the JPL Airborne Imaging Spectrometer and the Collins' Airborne Spectroradiometer are being used for forest species identification. The linear discriminant function has provided higher identification accuracies than have principal components analyses. Highest identification accuracies are obtained in the 450 to 520 nm spectral region. Spectral bands near 1,300, 1,685 and 2,220 nm appear to be important, also

Report of Acoustic Test on PSLV IS.1/2L Structure

The results of acoustic conducted on PSLV IS.1/2L at Acoustic Test Facility are briefly given. It contains test set up, Instrumentation details and tables of spectral response

Detecting long-range dependence in non-stationary time series

An important problem in time series analysis is the discrimination between non-stationarity and longrange dependence. Most of the literature considers the problem of testing specific parametric hypotheses of non-stationarity (such as a change in the mean) against long-range dependent stationary alternatives. In this paper we suggest a simple approach, which can be used to test the null-hypothesis of a general non-stationary short-memory against the alternative of a non-stationary long-memory process. The test procedure works in the spectral domain and uses a sequence of approximating tvFARIMA models to estimate the time varying long-range dependence parameter. We prove uniform consistency of this estimate and asymptotic normality of an averaged version. These results yield a simple test (based on the quantiles of the standard normal distribution), and it is demonstrated in a simulation study that - despite of its semi-parametric nature - the new test outperforms the currently available methods, which are constructed to discriminate between specific parametric hypotheses of non-stationarity short- and stationarity long-range dependence.Comment: Keywords and phrases: spectral density, long-memory, non-stationary processes, goodness-of-fit tests, empirical spectral measure, integrated periodogram, locally stationary process, approximating model