Critical earthquake input power spectral density function models for engineering structures

The problem of determining optimal power spectral density models for earthquake excitation which satisfy constraints on total average power, zero crossing rate and which produce the highest response variance in a given linear system is considered. The solution to this problem is obtained using linear programming methods. The resulting solutions are shown to display a highly deterministic structure and, therefore, fail to capture the stochastic nature of the input. A modification to the definition of critical excitation is proposed which takes into account the entropy rate as a measure of uncertainty in the earthquake loads. The resulting problem is solved using calculus of variations and also within linear programming framework. Illustrative examples on specifying seismic inputs for a nuclear power plant and a tall earth dam are considered and the resulting solutions are shown to be realistic.

Parallel implementation of the recurrence method for computing the power-spectral density of thin avalanche photodiodes

A simulation program has been developed to calculate the power-spectral density of thin avalanche photodiodes, which are used in optical networks. The program extends the time-domain analysis of the dead-space multiplication model to compute the autocorrelation function of the APD impulse response. However, the computation requires a large amount of memory space and is very time consuming. We describe our experiences in parallelizing the code using both MPI and OpenMP. Several array partitioning schemes and scheduling policies are implemented and tested Our results show that the OpenMP code is scalable up to 64 processors on an SGI Origin 2000 machine and has small average errors.

Power Spectral Density Side-Channel Attack Overlapping Window Method

Cryptographic algorithms have been designed to be computationally secure, however it has been shown that when they are implemented in hardware, that these devices leak side channel information that can be used to mount an attack that recovers the secret encryption key. In this paper an overlapping window power spectral density (PSD) side channel attack, targeting an FPGA device running the Advanced Encryption Standard is proposed. This improves upon previous research into PSD attacks by reducing the amount of pre-processing (effort) required. It is shown that the proposed overlapping window method requires less processing effort than that of using a sliding window approach, whilst overcoming the issues of sampling boundaries. The method is shown to be effective for both aligned and misaligned data sets and is therefore recommended as an improved approach in comparison with existing time domain based correlation attacks.

Variable Window Power Spectral Density Attack

Side channel attacks permit the recovery of the secret key held within a cryptographic device. This paper presents a new EM attack in the frequency domain, using a power spectral density analysis that permits the use of variable spectral window widths for each trace of the data set and demonstrates how this attack can therefore overcome both inter-and intra-round random insertion type countermeasures. We also propose a novel re-alignment method exploiting the minimal power markers exhibited by electromagnetic emanations. The technique can be used for the extraction and re-alignment of round data in the time domain.

Effect of two-level systems on the spectral density of universal conductance fluctuations in doped Si

We have studied the power spectral density [S(f) = gamma/f(alpha)] of universal conductance fluctuations (UCF's) in heavily doped single crystals of Si, when the scatterers themselves act as the primary source of dephasing. We observed that the scatterers, with internal dynamics like two-level-systems, produce a significant, temperature-dependent reduction in the spectral slope alpha when T less than or similar to 10 K, as compared to the bare 1/f (alphaapproximate to1) spectrum at higher temperatures. It is further shown that an upper cutoff frequency (f(m)) in the UCF spectrum is necessary in order to restrict the magnitude of conductance fluctuations, [(deltaG(phi))(2)], per phase coherent region (L-phi(3)) to [(deltaGphi)(2)](1/2) less than or similar to e(2)/h. We find that f(m) approximate to tau(D)(-1), where tau(D) = L-2/D, is the time scale of the diffusive motion of the electron along the active length (L) of the sample (D is the electron diffusivity).

Spectral density enhancement using coherent WDM

It is shown by numerical simulations that a significant increase in the spectral density of a 40-Gb/s wavelength-division-multiplexing (WDM) system can be obtained by controlling the phase of adjacent WDM channels. These simulations are confirmed experimentally at 40 Gb/s using a coherent,comb source. This technique allows the spectral density of a nonreturn-to-zero WDM system to be increased from 0.4 to 1 b/s/Hz in a single polarization. Optical filter optimization is required to minimize power crosstalk, and appropriate strategies are discussed in this letter. Index Terms-Filtering, optical communication terminals, phase control, wavelength-division multiplexing (WDM).

Multivariate Granger causality: an estimation framework based on factorization of the spectral density matrix

Granger causality is increasingly being applied to multi-electrode neurophysiological and functional imaging data to characterize directional interactions between neurons and brain regions. For a multivariate dataset, one might be interested in different subsets of the recorded neurons or brain regions. According to the current estimation framework, for each subset, one conducts a separate autoregressive model fitting process, introducing the potential for unwanted variability and uncertainty. In this paper, we propose a multivariate framework for estimating Granger causality. It is based on spectral density matrix factorization and offers the advantage that the estimation of such a matrix needs to be done only once for the entire multivariate dataset. For any subset of recorded data, Granger causality can be calculated through factorizing the appropriate submatrix of the overall spectral density matrix.

Optimal input cross-power spectra in shake table testing of asymmetric structures

The study considers earthquake shake table testing of bending-torsion coupled structures under multi-component stationary random earthquake excitations. An experimental procedure to arrive at the optimal excitation cross-power spectral density (psd) functions which maximize/minimize the steady state variance of a chosen response variable is proposed. These optimal functions are shown to be derivable in terms of a set of system frequency response functions which could be measured experimentally without necessitating an idealized mathematical model to be postulated for the structure under study. The relationship between these optimized cross-psd functions to the most favourable/least favourable angle of incidence of seismic waves on the structure is noted. The optimal functions are also shown to be system dependent, mathematically the sharpest, and correspond to neither fully correlated motions nor independent motions. The proposed experimental procedure is demonstrated through shake table studies on two laboratory scale building frame models.

Spectral density of first order Piecewise linear systems excited by white noise

The Fokker-Planck (FP) equation is used to develop a general method for finding the spectral density for a class of randomly excited first order systems. This class consists of systems satisfying stochastic differential equations of form ẋ + f(x) = m/Ʃ/j = 1 h_j(x)n_j(t) where f and the h_j are piecewise linear functions (not necessarily continuous), and the n_j are stationary Gaussian white noise. For such systems, it is shown how the Laplace-transformed FP equation can be solved for the transformed transition probability density. By manipulation of the FP equation and its adjoint, a formula is derived for the transformed autocorrelation function in terms of the transformed transition density. From this, the spectral density is readily obtained. The method generalizes that of Caughey and Dienes, J. Appl. Phys., 32.11.

This method is applied to 4 subclasses: (1) m = 1, h₁ = const. (forcing function excitation); (2) m = 1, h₁ = f (parametric excitation); (3) m = 2, h₁ = const., h₂ = f, n₁ and n₂ correlated; (4) the same, uncorrelated. Many special cases, especially in subclass (1), are worked through to obtain explicit formulas for the spectral density, most of which have not been obtained before. Some results are graphed.

Dealing with parametrically excited first order systems leads to two complications. There is some controversy concerning the form of the FP equation involved (see Gray and Caughey, J. Math. Phys., 44.3); and the conditions which apply at irregular points, where the second order coefficient of the FP equation vanishes, are not obvious but require use of the mathematical theory of diffusion processes developed by Feller and others. These points are discussed in the first chapter, relevant results from various sources being summarized and applied. Also discussed is the steady-state density (the limit of the transition density as t → ∞).

Coherent wavelength division multiplexing: a novel transmission format for high spectral density optical communication networks

In this thesis a novel transmission format, named Coherent Wavelength Division Multiplexing (CoWDM) for use in high information spectral density optical communication networks is proposed and studied. In chapter I a historical view of fibre optic communication systems as well as an overview of state of the art technology is presented to provide an introduction to the subject area. We see that, in general the aim of modern optical communication system designers is to provide high bandwidth services while reducing the overall cost per transmitted bit of information. In the remainder of the thesis a range of investigations, both of a theoretical and experimental nature are carried out using the CoWDM transmission format. These investigations are designed to consider features of CoWDM such as its dispersion tolerance, compatibility with forward error correction and suitability for use in currently installed long haul networks amongst others. A high bit rate optical test bed constructed at the Tyndall National Institute facilitated most of the experimental work outlined in this thesis and a collaboration with France Telecom enabled long haul transmission experiments using the CoWDM format to be carried out. An amount of research was also carried out on ancillary topics such as optical comb generation, forward error correction and phase stabilisation techniques. The aim of these investigations is to verify the suitability of CoWDM as a cost effective solution for use in both current and future high bit rate optical communication networks

Adaptive modeling and high quality spectral estimation for speech enhancement

In this work an adaptive modeling and spectral estimation scheme based on a dual Discrete Kalman Filtering (DKF) is proposed for speech enhancement. Both speech and noise signals are modeled by an autoregressive structure which provides an underlying time frame dependency and improves time-frequency resolution. The model parameters are arranged to obtain a combined state-space model and are also used to calculate instantaneous power spectral density estimates. The speech enhancement is performed by a dual discrete Kalman filter that simultaneously gives estimates for the models and the signals. This approach is particularly useful as a pre-processing module for parametric based speech recognition systems that rely on spectral time dependent models. The system performance has been evaluated by a set of human listeners and by spectral distances. In both cases the use of this pre-processing module has led to improved results.