Higher order spectral (HOS) techniques, such as the bispectrum, offer robustness to Gaussian noise and the ability to recover phase information. However, their drawbacks, such as the high variance of estimates and the need for long data records, have limited their use in conventional speech processing applications. As in glottal pulse estimation, all existing inverse filtering approaches use se...

Composite linear and quadratic systems produce three-wave coupling when stimulated by random-phase input sinusoids. Due to the non-linearity of the system the output frequencies are arithmetically related to the input. Using third order cumulant statistics and their associated bispectrum, techniques are devised based on phaseinsensitive matrix structures for detection and frequency estimation o...

In this paper the third order long-range dependence (LRD) is de…ned in terms of the bispectrum and third order cumulants (bicovariances). Two particular non-Gaussian processes with second order LRD are considered together with their bispectra and bicovariances. AMS 2000 Subject Classi…cations: Primary 62M10, 37M10; secondary 62M15, 91B70. Dedicated to Endre Csáki and Pál Révész on the occasion ...

We study whether the bias factors of galaxies can be unbiasedly recovered from their power spectra and bispectra. We use a set of numericalN -body simulations and construct large mock galaxy catalogs based upon the semi-analytical model of Croton et al. (2006). We measure the reduced bispectra for galaxies of different luminosity, and determine the linear and first nonlinear bias factors from t...

We present theoretical and observational studies of non-Gaussian fluctuations in the cosmic microwave background (CMB) radiation anisotropy. We use the angular bispectrum and trispectrum, the harmonic transform of the angular threeand four-point correlation functions. If the primordial fluctuations are non-Gaussian, then this non-Gaussianity will be apparent in the CMB sky. Non-linearity in inf...

At high angular frequencies, beyond the damping tail of the primary cosmic microwave background (CMB) power spectrum, the thermal Sunyaev–Zel’dovich (tSZ) effect constitutes the dominant signal in the CMB sky. The tSZ effect is caused by large-scale pressure fluctuations in the baryonic distribution in the universe, such that its statistical properties provide estimates of corresponding propert...

The bispectrum of galaxies is a powerful probe of the non-linear gravitational evolution and galaxy formation. Non-linear evolution and non-linear galaxy biasing yield a non-vanishing bispectrum even in the absence of primordial nonGaussianity. Despite its promise, measurements of the bispectrum have been a challenge due to complicated window function effects and the covariance matrix. Here, we...