On the limits of spectral methods for frequency estimation

An algorithm is presented which generates pairs of oscillatory random time series which have identical periodograms but differ in the number of oscillations. This result indicates the intrinsic limitations of spectral methods when it comes to the task of measuring frequencies. Other examples, one from medicine and one from bifurcation theory, are given, which also exhibit these limitations of spectral methods. For two methods of spectral estimation it is verified that the particular way end points are treated, which is specific to each method, is, for long enough time series, not relevant for the main result.

A frequency measure robust to linear filtering

It is noted that the determination of an oscillation frequency by used of the power spectrum of measured time series is susceptible to filtering of the signal. Similarly, frequency measurements made by period counting can yield different, results depending on how the signal is filtered for noise reduction. In an attempt to eliminate these ambiguities, a new measure of frequency, based on an approximate reconstruction of the phase-space trajectory of the oscillator from the signal, is introduced. This measure is shown to be invariant under linear filtering. For this reason, it is also inaccessible by spectral methods. The effect of filtering on frequency for weakly nonlinear, noisy oscillators, to which this definition applies only imperfectly, is quantified. This work provides the theoretical basis for frequency measurements employing MIRVA filtering.

Discretization and solution of the inhomogeneous Bogoliubov-de Gennes equations

In the presence of inhomogeneities, defects and currents, the equations describing a Bose-condensed ensemble of alkali atoms have to be solved numerically. By combining both linear and nonlinear equations within a Discrete Variable Representation framework, we describe a computational scheme for the solution of the coupled Bogoliubov-de Gennes (BdG) and nonlinear Schrodinger (NLS) equations for fields in a 3D spheroidal potential. We use the method to calculate the collective excitation spectrum and quasiparticle mode densities for excitations of a Bose condensed gas in a spheroidal trap. The method is compared against finite-difference and spectral methods, and we find the DVR computational scheme to be superior in accuracy and efficiency for the cases we consider. (C) 2004 Elsevier B.V. All rights reserved.

Design and evaluation of tinnitus synthesis methods: From spectral to spatial matching

Purpose
This study was designed to investigate methods to help patients suffering from unilateral tinnitus synthesizing an auditory replica of their tinnitus.

Materials and methods
Two semi-automatic methods (A and B) derived from the auditory threshold of the patient and a method (C) combining a pure tone and a narrow band-pass noise centred on an adjustable frequency were devised and rated on their likeness over two test sessions. A third test evaluated the stability over time of the synthesized tinnitus replica built with method C, and its proneness to merge with the patient's tinnitus. Patients were then asked to try and control the lateralisation of this single percept through the adjustment of the tinnitus replica level.

Results
The first two tests showed that seven out of ten patients chose the tinnitus replica built with method C as their preferred one. The third test, performed on twelve patients, revealed pitch tuning was rather stable over a week interval. It showed that eight patients were able to consistently match the central frequency of the synthesized tinnitus (presented to the contralateral ear) to their own tinnitus, which leaded to a unique tinnitus percept. The lateralisation displacement was consistent across patients and revealed an average range of 29dB to obtain a full lateral shift from the ipsilateral to the contralateral side.

Conclusions
Although spectrally simpler than the semi-automatic methods, method C could replicate patients' tinnitus, to some extent. When a unique percept between synthesized tinnitus and patients' tinnitus arose, lateralisation of this percept was achieved.

Extended spectral decompositions of the Renyi map

We present new general methods to obtain spectral decompositions of dynamical systems in rigged Hilbert spaces and investigate the existence of resonances and the completeness of the associated eigenfunctions. The results are illustrated explicitly for the simplest chaotic endomorphism, namely the Renyi map.

Spectral induced polarization signatures of abiotic FeS precipitation

In recent years, geophysical methods have been shown to be sensitive to microbial-induced mineralization processes. The spectral induced-polarization (SIP) method appears to be very promising for monitoring mineralization and microbial processes. With this work, we study the links of mineralization and SIP signals, in the absence of microbial activity. We recorded the SIP response during abiotic FeS precipitation. We show that the SIP signals are diagnostic of FeS mineralization and can be differentiated from SIP signals from biomineralization processes. More specifically, the imaginary conductivity shows almost linear dependence on the amount of FeS precipitating out of solution, above the threshold value 0.006 gr under our experimental conditions. This research has direct implications for the use of the SIP method as a monitoring and decision-making tool for sustainable remediation of metals in contaminated soils and groundwater.

A new algorithm for spectral and spatial reconstruction of proton beams from dosimetric measurements

We report on a new algorithm developed for the dosimetric analysis of broad-spectrum, multi-MeV laser-accelerated proton beams. The algorithm allows the reconstruction of the proton beam spectrum from radiochromic film data. This processing technique makes dosimetry measurements a viable alternative to the use of track detectors for spatially and spectrally resolved proton beam analysis. (C) 2003 Elsevier B.V. All rights reserved.

A spectral synthesis code for rapid modelling of supernovae

We present TARDIS-an open-source code for rapid spectral modelling of supernovae (SNe). Our goal is to develop a tool that is sufficiently fast to allow exploration of the complex parameter spaces of models for SN ejecta. This can be used to analyse the growing number of highquality SN spectra being obtained by transient surveys. The code uses Monte Carlo methods to obtain a self-consistent description of the plasma state and to compute a synthetic spectrum. It has a modular design to facilitate the implementation of a range of physical approximations that can be compared to assess both accuracy and computational expediency. This will allow users to choose a level of sophistication appropriate for their application. Here, we describe the operation of the code and make comparisons with alternative radiative transfer codes of differing levels of complexity (SYN++, PYTHON and ARTIS). We then explore the consequence of adopting simple prescriptions for the calculation of atomic excitation, focusing on four species of relevance to Type Ia SN spectra-Si II, SII, MgII and Ca II. We also investigate the influence of three methods for treating line interactions on our synthetic spectra and the need for accurate radiative rate estimates in our scheme.

A quality-scalable and energy-efficient approach for spectral analysis of heart rate variability

Today there is a growing interest in the integration of health monitoring applications in portable devices necessitating the development of methods that improve the energy efficiency of such systems. In this paper, we present a systematic approach that enables energy-quality trade-offs in spectral analysis systems for bio-signals, which are useful in monitoring various health conditions as those associated with the heart-rate. To enable such trade-offs, the processed signals are expressed initially in a basis in which significant components that carry most of the relevant information can be easily distinguished from the parts that influence the output to a lesser extent. Such a classification allows the pruning of operations associated with the less significant signal components leading to power savings with minor quality loss since only less useful parts are pruned under the given requirements. To exploit the attributes of the modified spectral analysis system, thresholding rules are determined and adopted at design- and run-time, allowing the static or dynamic pruning of less-useful operations based on the accuracy and energy requirements. The proposed algorithm is implemented on a typical sensor node simulator and results show up-to 82% energy savings when static pruning is combined with voltage and frequency scaling, compared to the conventional algorithm in which such trade-offs were not available. In addition, experiments with numerous cardiac samples of various patients show that such energy savings come with a 4.9% average accuracy loss, which does not affect the system detection capability of sinus-arrhythmia which was used as a test case. 

Polarization spectral synthesis for Type Ia supernova explosion models

We present a Monte Carlo radiative transfer technique for calculating synthetic spectropolarimetry for multidimensional supernova explosion models. The approach utilizes 'virtual-packets' that are generated during the propagation of the Monte Carlo quanta and used to compute synthetic observables for specific observer orientations. Compared to extracting synthetic observables by direct binning of emergent Monte Carlo quanta, this virtual-packet approach leads to a substantial reduction in the Monte Carlo noise. This is not only vital for calculating synthetic spectropolarimetry (since the degree of polarization is typically very small) but also useful for calculations of light curves and spectra. We first validate our approach via application of an idealized test code to simple geometries. We then describe its implementation in the Monte Carlo radiative transfer code ARTIS and present test calculations for simple models for Type Ia supernovae. Specifically, we use the well-known one-dimensional W7 model to verify that our scheme can accurately recover zero polarization from a spherical model, and to demonstrate the reduction in Monte Carlo noise compared to a simple packet-binning approach. To investigate the impact of aspherical ejecta on the polarization spectra, we then use ARTIS to calculate synthetic observables for prolate and oblate ellipsoidal models with Type Ia supernova compositions.