Parametric spectral analysis: scale and shift

We introduce the paradigm of dilation and translation for use in the spectral analysis of complex-valued univariate or multivariate data. The new procedure stems from a search on how to solve ambiguity problems in this analysis, such as aliasing because of too coarsely sampled data, or collisions in projected data, which may be solved by a translation of the sampling locations. In Section 2 both dilation and translation are first presented for the classical one-dimensional exponential analysis. In the subsequent Sections 3--7 the paradigm is extended to more functions, among which the trigonometric functions cosine, sine, the hyperbolic cosine and sine functions, the Chebyshev and spread polynomials, the sinc, gamma and Gaussian function, and several multivariate versions of all of the above. Each of these function classes needs a tailored approach, making optimal use of the properties of the base function used in the considered sparse interpolation problem. With each of the extensions a structured linear matrix pencil is associated, immediately leading to a computational scheme for the spectral analysis, involving a generalized eigenvalue problem and several structured linear systems. In Section 8 we illustrate the new methods in several examples: fixed width Gaussian distribution fitting, sparse cardinal sine or sinc interpolation, and lacunary or supersparse Chebyshev polynomial interpolation

The Influence Of Knowledge Management On Market-Related Performance Through Business Process Effectiveness: An Empirical Investigation Of Hospitals And Financial Firms

Knowledge-based resources are critical in service sectors for facing the challenges of dynamic markets and helping organizations manage changes in consumer preference. Knowledge application is needed to improve the business process in order to attain superior market-related performance because there is the unperfected imitation coming from causal ambiguity. However, there is a lack of empirical study in examining the effect of KM and the effect of the business process within the scope of service sectors. This study examines how KM infrastructure supports and KM capabilities influence market-related performance through business processes effectiveness. Data collections of two studies are from 166 hospitals and 106 financial firms. The findings indicate a positive relationship between KM infrastructure and KM capability, and that they have a positive influence on market-related performance through business process effectiveness. For improving this process, the effect of KM infrastructure is greater than the effect of KM capabilities in hospitals. But the effect of KM capabilities is greater than the effect of KM infrastructure in financial firms. The implications of these findings for research and practices in hospitals and financial firms are also discussed

Validated exponential analysis for harmonic sounds

In audio spectral analysis, the Fourier method is popular because of its stability and its low computational complexity. It suffers however from a time-frequency resolution trade off and is not particularly suited for aperiodic signals such as exponentially decaying ones. To overcome their resolution limitation, additional techniques such as quadratic peak interpolation or peak picking, and instantaneous frequency computation from phase unwrapping are used. Parametric methods on the other hand, overcome the time frequency trade off but are more susceptible to noise and have a higher computational complexity. We propose a method to overcome these drawbacks: we set up regularized smaller sized independent problems and perform a cluster analysis on their combined output. The new approach validates the true physical terms in the exponential model, is robust in the presence of outliers in the data and is able to filter out any non-physical noise terms in the model. The method is illustrated in the removal of electrical humming in harmonic sounds

A short-time Prony method for the detection of transients

Many parametric spectral methods are based on the classical algorithm of the French engineer G. de Prony for exponential analysis. A drawback of this method is that it cannot take into consideration any discontinuities due to the starting and ending of the exponential components at different instants. We introduce a short-time Prony method that allows to extract the characteristics from such a signal and we illustrate the new method on a number of power system signals. All parameters in the signals can be extracted with high accuracy and we show how to monitor the occurrence of the transients dynamically

Sparse multidimensional exponential analysis with an application to radar imaging

We present a d-dimensional exponential analysis algorithm that offers a range of advantages compared to other methods. The technique does not suffer the curse of dimensionality and only needs O((d + 1)n) samples for the analysis of an n-sparse expression. It does not require a prior estimate of the sparsity n of the d-variate exponential sum. The method can work with sub-Nyquist sampled data and offers a validation step, which is very useful in low SNR conditions. A favourable computation cost results from the fact that d independent smaller systems are solved instead of one large system incorporating all measurements simultaneously. So the method also lends itself easily to a parallel execution. Our motivation to develop the technique comes from 2D and 3D radar imaging and is therefore illustrated on such examples

Sparse Modelling and Multi-exponential Analysis

The research fields of harmonic analysis, approximation theory and computer algebra are seemingly different domains and are studied by seemingly separated research communities. However, all of these are connected to each other in many ways. The connection between harmonic analysis and approximation theory is not accidental: several constructions among which wavelets and Fourier series, provide major insights into central problems in approximation theory. And the intimate connection between approximation theory and computer algebra exists even longer: polynomial interpolation is a long-studied and important problem in both symbolic and numeric computing, in the former to counter expression swell and in the latter to construct a simple data model. A common underlying problem statement in many applications is that of determining the number of components, and for each component the value of the frequency, damping factor, amplitude and phase in a multi-exponential model. It occurs, for instance, in magnetic resonance and infrared spectroscopy, vibration analysis, seismic data analysis, electronic odour recognition, keystroke recognition, nuclear science, music signal processing, transient detection, motor fault diagnosis, electrophysiology, drug clearance monitoring and glucose tolerance testing, to name just a few. The general technique of multi-exponential modeling is closely related to what is commonly known as the Padé-Laplace method in approximation theory, and the technique of sparse interpolation in the field of computer algebra. The problem statement is also solved using a stochastic perturbation method in harmonic analysis. The problem of multi-exponential modeling is an inverse problem and therefore may be severely ill-posed, depending on the relative location of the frequencies and phases. Besides the reliability of the estimated parameters, the sparsity of the multi-exponential representation has become important. A representation is called sparse if it is a combination of only a few elements instead of all available generating elements. In sparse interpolation, the aim is to determine all the parameters from only a small amount of data samples, and with a complexity proportional to the number of terms in the representation. Despite the close connections between these fields, there is a clear lack of communication in the scientific literature. The aim of this seminar is to bring researchers together from the three mentioned fields, with scientists from the varied application domains.Output Type: Meeting Repor

Multiple sclerosis presenting with homonymous hemianopia

Ophthalmic manifestations are a prominent feature of multiple sclerosis (MS). Optic neuritis accounts for 18% of initial MS symptoms and 40–70% of all patients with MS have at least one episode of optic neuritis during their disease course. Eye movement abnormalities such as internuclear ophthalmoplegia are seen in over 50% of patients with MS. This case study describes a rare initial presentation of MS with ‘left eye blurred vision’ and examination findings of a complete left homonymous hemianopia. Although homonymous hemianopia is uncommon (0.5–3.5% of MS cases), this case highlights an important reminder that people with a field defect often complain of ‘blurred vision’ on the side of the defect

Degree-degree Correlated Low-density Parity-check Codes Over a Binary Erasure Channel

Most existing works on analyzing the performance of a random ensemble of low-density parity-check (LDPC) codes assume that the degree distributions of the two ends of a randomly selected edge are independent. In the paper, we take one step further and consider ensembles of LDPC codes with degree-degree correlations. For this, we propose two methods to construct an ensemble of degree-degree correlated LDPC codes. We then derive a system of density evolution equations for such degree-degree correlated LDPC codes over a binary erasure channel (BEC). By conducting extensive numerical experiments, we show how the degree-degree correlation affects the performance of LDPC codes. Our numerical results show that LDPC codes with negative degree-degree correlation could improve the maximum tolerable erasure probability. Moreover, increasing the negative degree-degree correlation could lead to better unequal error protection (UEP) design.Comment: accepted by the 2023 IEEE International Symposium on Information Theory (ISIT