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A 3-D spatiotemporal prediction-error filter (PEF), is used to enhance foreground/background contrast in (real and simulated) sensor image sequences. Relative velocity is utilized to extract point-targets that would otherwise be…
We employ the variational formulation and the Euler-Lagrange equations to study the steady-state error in linear non-causal estimators (smoothers). We give a complete description of the steady-state error for inputs that are polynomial in…
In this paper we first introduce the setting of filtering on Stiefel manifolds. Then, assuming the underlying system process is constant, the convergence of the extended Kalman filter with Stiefel manifold-valued observations is proved.…
Filters from the Gammatone family are often used to model auditory signal processing, but the filter constant values used to mimic human hearing are largely set to values based on historical psychoacoustic data collected several decades…
State filtering is a key problem in many signal processing applications. From a series of noisy measurement, one would like to estimate the state of some dynamic system. Existing techniques usually adopt a Gaussian noise assumption which…
Despite being a foundational concept of modern systems theory, there have been few studies on observability of non-linear stochastic systems under partial observations. In this paper, we introduce a definition of observability for…
The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…
This technical note is on digital filters for the high-fidelity estimation of a sinusoidal signal's frequency in the presence of additive noise. The complex noise is assumed to be white (i.e. uncorrelated) however it need not be Gaussian.…
A standard finite element method discretizes the stochastic linear Schr\"{o}dinger equation driven by additive noise in the spatial variables. The weak convergence of the resulting approximate solution is analyzed, and it is established…
Any frequency selective device with an ongoing drift will cause observed spectra to be variously and simultaneously scaled in proportion to their source distances. The reason is that detectors after the drifting selection will integrate…
A stochastic model for a continuous photon counting and heterodyne measurement of a coherent source is proposed. A nonlinear filtering equation for the posterior state of a single-mode field in a cavity is derived by using the methods of…
As new techniques exploiting the Earth's ambient seismic noise field are developed and applied, such as for the observation of temporal changes in seismic velocity structure, it is crucial to quantify the precision with which wave-type…
The idealized theory of quantum vacuum energy density is a beautiful application of the spectral theory of differential operators with boundary conditions, but its conclusions are physically unacceptable. A more plausible model of a…
Time-domain chromatic dispersion (CD) equalization using finite impulse response (FIR) filter is now a common approach for coherent optical fiber communication systems. The complex weights of FIR filter taps are calculated from a truncated…
Motivated by the simulation of stable random fields, we consider the issue of discrete approximations of independently scattered stable noise. Two approaches are proposed: grid approximations available when the underlying space is $\bbR^d$…
Fluctuation spectra of fluid compound membrane systems are calculated. The systems addressed contain two (or more) almost parallel membranes that are connected by harmonic tethers or by a continuous, harmonic confining potential.…
This paper focuses on spectral filters on graphs, namely filters defined as elementwise multiplication in the frequency domain of a graph. In many graph signal processing settings, it is important to transfer a filter from one graph to…
Let f_n denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let \Psi(t) be a positive continuous function such that \|\Psi f^{\beta}\|_{\infty}<\infty for some 0<\beta<1/2. Under natural…
We provide a detailed description of the Herschel-SPIRE Fourier Transform Spectrometer (FTS) Spectral Feature Finder (FF). The FF is an automated process designed to extract significant spectral features from SPIRE FTS data products.…
A phase space formulation of the filtering process upon an incident quantum state is developed. This formulation can explain the results of both quantum interference and delayed-choice experiments without making use of the controversial…