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The rational covariance extension problem is to parametrize the family of rational spectra of bounded degree that matches a given set of covariances. This article treats a circulant version of this problem, where the underlying process is periodic and we seek a spectrum that also matches a set of given cepstral coefficients. The interest in the circulant problem stems partly from the fact that this problem is a natural approximation of the non-periodic problem, but is also a tool in itself for analysing periodic processes. We develop a fast Newton algorithm for computing the solution utilizing the structure of the Hessian. This is done by extending a current algorithm for Toeplitz-plus-Hankel systems to the block-Toeplitz-plus-block-Hankel case. We use this algorithm to reduce the computational complexity of the Newton search from O(n3) to O(n2), where n corresponds to the number of covariances and cepstral coefficients., QC 20160617

Partial stochastic realization of periodic processes from finite covariance data leads to the circulant rational covariance extension problem and bilateral ARMA models. In this paper we present a convex optimization-based theory for this problem that extends and modifies previous results by Carli, Ferrante, Pavon and Picci on the AR solution, which have been successfully applied to image processing of textures. We expect that our present results will provide an enhancement of these procedures., QC 20140911

The gravitational redshift forms the central part of the majority of the classical tests for the general theory of relativity. It could be successfully checked even in laboratory experiments on the earths surface. The standard derivation of this effect is based on the distortion of the local structure of spacetime induced by large masses. The resulting gravitational time dilation near these masses gives rise to a frequency change of any periodic process, including electromagnetic oscillations as the wave propagates across the gravitational field. This phenomenon can be tackled with classical electrodynamics assuming a curved spacetime background and Maxwells equations in a generally covariant form. In this paper, we show that in a classical field theoretical context the gravitational redshift can be interpreted as the propagation of electromagnetic waves in a medium with corresponding conductivity ¿ = g/(¿ 0c 3), where g is the gravitational acceleration and ¿ 0 is the vacuum magnetic permeability. Moreover, the energy density of the wave remains proportional to its frequency in agreement with Plancks postulate. © 2012 IOP Publishing Ltd.

One way to achieve process intensification is to operate the process in a periodic way, in order to obtain better average performance compared to the optimal steady-state operation. The source of the possible improvement lies in the process nonlinearity. Nevertheless, the improvement is obtained only in some cases, while in some others the periodic operation can be unfavourable. Testing whether a potential periodic process is favourable or unfavourable generally demands long and tedious experimental and/or numerical work. This paper presents a new, fast and easy method for this testing, based on the Volterra series approach, nonlinear frequency response and the concept of higher order frequency response functions.

One way to achieve process intensification is to operate the process in a periodic way, in order to obtain better average performance compared to the optimal steady-state operation. The source of the possible improvement lies in the process nonlinearity. Nevertheless, the improvement is obtained only in some cases, while in some others the periodic operation can be unfavourable. Testing whether a potential periodic process is favourable or unfavourable generally demands long and tedious experimental and/or numerical work. This paper presents a new, fast and easy method for this testing, based on the Volterra series approach, nonlinear frequency response and the concept of higher order frequency response functions.

One way to achieve process intensification is to operate the process in a periodic way, in order to obtain better average performance compared to the optimal steady-state operation. The source of the possible improvement lies in the process nonlinearity. Nevertheless, the improvement is obtained only in some cases, while in some others the periodic operation can be unfavourable. Testing whether a potential periodic process is favourable or unfavourable generally demands long and tedious experimental and/or numerical work. This paper presents a new, fast and easy method for this testing, based on the Volterra series approach, nonlinear frequency response and the concept of higher order frequency response functions.

One way to achieve process intensification is to operate the process in a periodic way, in order to obtain better average performance compared to the optimal steady-state operation. The source of the possible improvement lies in the process nonlinearity. Nevertheless, the improvement is obtained only in some cases, while in some others the periodic operation can be unfavourable. Testing whether a potential periodic process is favourable or unfavourable generally demands long and tedious experimental and/or numerical work. This paper presents a new, fast and easy method for this testing, based on the Volterra series approach, nonlinear frequency response and the concept of higher order frequency response functions.

A periodic process can be characterized in terms of three periodicity (or p-) attributes: the periodicity (or period-length), the periodic wave-shape or pattern and the wave-magnitude or the scaling factor; all three attributes can be time varying in a real-life situation. In this report, we hypothesize that an analysis of the dynamics underlying a nearly periodic physiological process, such as appearing in a rhythmic blood wave pattern, can be quantified in terms of the dynamics of its periodicity attributes. This report analyzes data obtained from archival studies in which the photo-plethysmograph signal (PPS) is recorded from the finger. Each specific blood wave signal is decomposed into a regular component, which is nearly periodic and an irregular residual process. The dynamics of the PPS p-attributes of the regular part are analyzed individually as well as collectively to assess the general cardiovascular state. A new class of surrogate series based on the shuffling of the p-attributes is proposed to detect the nonlinear determinism in the PPS. The dynamics is further studied by mapping the variations of the p-attributes in a novel p-space, defined by the three orthogonal periodicity-attribute components; each point in the p-space represents one nearly periodic segment. Novel complexity measures based on global and temporal variations 0 dynamics in the p-space are proposed. A correlation is explored between the complexity measures derived from the p-space mapping of PPS that closely matches the cardiovascular state of a typical human subject. The mathematical algorithms derived from a simple blood flow wave pattern can be easily applied for assessing other physiologic signals in the cardiovascular system obtained during perturbations caused by dynamic exercise, thermal stress, and potentially high terrestrial physiologic effects during hypobaric stress.