Search results for "Cross-correlation"
showing 10 items of 38 documents
Cross-correlation and cross-power spectral density representation by complex spectral moments
2017
Abstract A new approach to provide a complete characterization of normal multivariate stochastic vector processes is presented in this paper. Such proposed method is based on the evaluation of the complex spectral moments of the processes. These quantities are strictly related to the Mellin transform and they are the generalization of the integer-order spectral moments introduced by Vanmarcke. The knowledge of the complex spectral moments permits to obtain the power spectral densities and their cross counterpart by a complex series expansions. Moreover, with just the aid of some mathematical properties the complex fractional moments permit to obtain also the correlation and cross-correlatio…
Fluorescence Lifetime of a Single Molecule as an Observable of Meta-Basin Dynamics in Fluids Near the Glass Transition
2006
Using single molecule spectroscopy, we show that the fluorescence lifetime trajectories of single probe molecules embedded in a glass-forming polymer melt exhibit strong fluctuations of a hopping character. Using molecular dynamics simulations targeted to explain these experimental observations, we show that the lifetime fluctuations correlate strongly with the average square displacement function of the matrix particles. The latter observable is a direct probe of the meta-basin transitions in the potential energy landscape of glass-forming liquids. We thus show here that single molecule experiments can provide detailed microscopic information on system properties that hitherto have been ac…
Evolution of worldwide stock markets, correlation structure and correlation based graphs
2011
We investigate the daily correlation present among market indices of stock exchanges located all over the world in the time period Jan 1996 - Jul 2009. We discover that the correlation among market indices presents both a fast and a slow dynamics. The slow dynamics reflects the development and consolidation of globalization. The fast dynamics is associated with critical events that originate in a specific country or region of the world and rapidly affect the global system. We provide evidence that the short term timescale of correlation among market indices is less than 3 trading months (about 60 trading days). The average values of the non diagonal elements of the correlation matrix, corre…
Evolution of correlation structure of industrial indices of U.S. equity markets
2013
We investigate the dynamics of correlations present between pairs of industry indices of US stocks traded in US markets by studying correlation based networks and spectral properties of the correlation matrix. The study is performed by using 49 industry index time series computed by K. French and E. Fama during the time period from July 1969 to December 2011 that is spanning more than 40 years. We show that the correlation between industry indices presents both a fast and a slow dynamics. The slow dynamics has a time scale longer than five years showing that a different degree of diversification of the investment is possible in different periods of time. On top to this slow dynamics, we als…
Comparison of the dynamics of the AU and PC indices
1998
The properties of AU and PC data were analyzed with different methods. It is shown that the dynamical behavior of the AU and PC time series, as analyzed by the structure function (SF), are very similar, while the SF of the AL time series shows different behavior. The SF of the AL data has a slope of 0.5 up to about 2 hours, after which it quickly decreases to about 0.1. On the other hand the slope of the SFs of AU and PC data continuously decreases to about 0.2, and in a longer time scale. It is suggested that the dissipative auroral electrojet currents have a characteristic time scale of 2 hours, and this underlies the AL dynamics. In contrast with this, the nondissipative Hall currents th…
Imaging Trapped Ion Structures via Fluorescence Cross-Correlation Detection
2021
Cross-correlation signals are recorded from fluorescence photons scattered in free space off a trapped ion structure. The analysis of the signal allows for unambiguously revealing the spatial frequency, thus the distance, as well as the spatial alignment of the ions. For the case of two ions we obtain from the cross-correlations a spatial frequency ${f}_{\text{spatial}}=1490\ifmmode\pm\else\textpm\fi{}{2}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{8}_{\mathrm{syst}}\text{ }\text{ }{\mathrm{rad}}^{\ensuremath{-}1}$, where the statistical uncertainty improves with the integrated number of correlation events as ${N}^{\ensuremath{-}0.51\ifmmode\pm\else\textpm\fi{}0.06}$. We independently deter…
Detection of events by means of plane wave decomposition analysis and cross-correlation technniques using a circular array of microphones
2013
[EN] This article deals with the study and analysis of room acoustics through a process of sound field decomposition sampled with microphones circular arrays. The spatial characteristics of the sound field inside a room can be meaningfully described by means of microphone array processing techniques. In this context, the set of impulse responses sampled by a microphone array can be seen as an image made of acoustic planewave footprints. Due to the circular geometry of the microphone array, these footprints have a cosine-like shape that can be fully described as a function of the direction of arrival (DOA) of the impinging plane wave.Plane-wave decomposition (PWD) technique using microphone …
Wavelet correlation filter for wide-angle seismic data
2002
A new filtering technique for single-fold wide-angle reflection/refraction seismic data is presented. The technique is based on the wavelet decomposition of a set of adjacent traces followed by coherence analysis. The filtering procedure consists of three steps. In the first, a wavelet decomposition of traces into different detail levels is performed. In the second, the coherence attributes for each level are evaluated by calculating cross-correlation functions of detail portions contained in a space–time moving window. Finally, the filtered traces are obtained as a weighted reconstruction of the trace details. Each weight is obtained from the coherence-attributes distribution estimated in …
Frequency-Sliding Generalized Cross-Correlation: A Sub-Band Time Delay Estimation Approach
2020
The generalized cross correlation (GCC) is regarded as the most popular approach for estimating the time difference of arrival (TDOA) between the signals received at two sensors. Time delay estimates are obtained by maximizing the GCC output, where the direct-path delay is usually observed as a prominent peak. Moreover, GCCs play also an important role in steered response power (SRP) localization algorithms, where the SRP functional can be written as an accumulation of the GCCs computed from multiple sensor pairs. Unfortunately, the accuracy of TDOA estimates is affected by multiple factors, including noise, reverberation and signal bandwidth. In this paper, a sub-band approach for time del…
A modal approach for the evaluation of the response sensitivity of structural systems subjected to non-stationary random processes
2005
A method for the evaluation of the response sensitivity of both classically and non-classically damped discrete linear structural systems under stochastic actions is presented. The proposed approach requires the following items: (a) a suitable modal expansion of the response; (b) the derivation in analytical form of the equations governing the evolution of the derivatives of the response (the so-called sensitivity equations) with respect to the parameters that define the structural model; (c) an extensive use of the Kronecker algebra for determining the analytical expressions of the sensitivity of the structural response statistics to non-stationary random input processes. Moreover, a step-…