Consider two multi-dimensional digital signals, each with Ns samples. For some number of lags Nl Ns, the cost of computing a single cross-correlation of these two signals is proportional to Ns ×Nl. By exploiting several properties of Gaussian windows, we can compute Ns local cross-correlations, again with computational cost proportional to Ns×Nl. Here, local means the cross-correlation of signa...

Inter-aural time differences (ITDs) constitute an important localization cue for azimuth estimation, particularly below 1.5 kHz. As a first approximation, it is commonly assumed that ITDs do not depend on frequency. Nevertheless, Kuhn (JASA, 1977) shows theoretically and experimentally that due to diffraction effects around the head, ITDs depend on frequency. Low frequency ITDs should thus theo...

A typical imaging condition for seismic reflection data involves source and receiver wavefield matching, e.g. by cross-correlation, at every image location. This statement is true no matter how the two wavefields are reconstructed, for example by one-way wavefield extrapolation, or two-way reverse-time extrapolation, or Kirchhoff integral methods. This statement is also true when the source and...

Canonical correlation analysis is a widely used multivariate statistical technique for exploring the relation between two sets of variables. This paper considers the problem of estimating the leading canonical correlation directions in high dimensional settings. Recently, under the assumption that the leading canonical correlation directions are sparse, various procedures have been proposed for...

where x̄ is the complex conjugate of x This paper uses the machinery of almost periodic functions to prove that even without uniform convergence the connection between a pair of almost periodic functions and the constants of the associated Fourier series exists for both the convolution and cross-correlation. The general results for two almost periodic functions are narrowed and applied to Ramanu...

Computational sound localisation using binaural microphones requires accurate Interaural Time Difference (ITD) estimation in order to infer an angle of incidence. The Phase Transform weighting function, used in generalized cross correlation calculations for microphone arrays is investigated here for application to ITD estimation in binaural head recordings. Empirical measurements using the meth...

A typical imaging condition for seismic reflection data involves source and receiver wavefield matching, e.g. by cross-correlation, at every image location. This statement is true no matter how the two wavefields are reconstructed, for example by one-way wavefield extrapolation, or two-way reverse-time extrapolation, or Kirchhoff integral methods. This statement is also true when the source and...

the electronic absorption spectral line shape of a diatomic molecule with harmonic potential curves is calculated using the time correlation function formalism. both the equilibrium shift and the frequency shift of the two linking electronic states ate taken into account. the spectrum is also calculated using the cumulated expansion which is related to the correlation function of the time-depen...

This article studies the convolutional kernel function of fractal operators in bone fibers. On basis micro-nano composite structure compact bone, we abstracted physical space fibers and derived operators. The aims to construct analytical expression proves that error is core component convolution In other words, mechanics fractional controlled by function.