Hidden Markov modeling of speech waveforms is studied and applied to speech recognition of clean and noisy signals. Signal vectors in each state are assumed Gaussian with zero mean and a Toeplitz covariance matrix. This model allows short signal vectors and thus is useful for speech signals with rapidly changing second order statistics. It can also be straightforwardly adapted to noisy signals ...

We provide a generalisation of Pinelis’ Rademacher-Gaussian tail comparison to complex coefficients. also establish uniform bounds on the probability that magnitude weighted sums independent random vectors Euclidean spheres with matrix coefficients exceeds its second moment.

We prove that iid random vectors that satisfy a rather weak moment assumption can be used as measurement vectors in Compressed Sensing, and the number of measurements required for exact reconstruction is the same as the best possible estimate – exhibited by a random Gaussian matrix. We then show that this moment condition is necessary, up to a log log factor. In addition, we explore the Compati...

We uncover geometric aspects that underlie the sum of two independent stochastic variables when both are governed by q−Gaussian probability distributions. The pertinent discussion is given in terms of random vectors uniformly distributed on a p−sphere.

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We consider a distributed source coding problem of L correlated Gaussian observations Yi, i = 1, 2, · · · , L. We assume that the random vector Y L = t(Y1, Y2, · · · , YL) is an observation of the Gaussian random vector X = t(X1, X2, · · · , XK), having the form Y L = AX +N , where A is a L×K matrix and N = t(N1, N2, · · · , NL) is a vector of L independent Gaussian random variables also indepe...

We propose a novel representation of cosmic microwave anisotropy maps, where each multipole order , is represented by , unit vectors pointing in directions on the sky and an overall magnitude. These ‘‘multipole vectors and scalars’’ transform as vectors under rotations. Like the usual spherical harmonics, multipole vectors form an irreducible representation of the proper rotation group SO(3). H...

We present a model for representing stationary multivariate time series with arbitrary marginal distributions and autocorrelation structures and describe how to generate data quickly and accurately to drive computer simulations. The central idea is to transform a Gaussian vector autoregressive process into the desired multivariate time-series input process that we presume as having a VARTA (Vec...

We review Maxwell’s multipole vectors, and elucidate some of their mathematical properties, with emphasis on the application of this tool to the cosmic microwave background (CMB). In particular, for a completely random function on the sphere (corresponding to the statistically isotropic Gaussian model of the CMB), we derive the full probability density function of the multipole vectors. This fu...