Frequency responses and resolving power of numerical integration of sampled data

Integration of sampled data arises in many practical applications, where the integrand function is available from experimental measurements only. One extensive field of research is the problem of pest monitoring and control where an accurate evaluation of the population size from the spatial density distribution is required for a given pest species. High aggregation population density distributions (peak functions) are an important class of data that often appear in this problem. The main difficulty associated with the integration of such functions is that the function values are usually only available at a few locations; therefore, new techniques are required to evaluate the accuracy of integration as the standard approach based on convergence analysis does not work when the data are sparse. Thus, in this paper, we introduce the new concept of ultra-coarse grids for high aggregation density distributions. Integration of the density function on ultra-coarse grids cannot provide the prescribed accuracy because of insufficient information (uncertainty) about the integrand function. Instead, the results of the integration should be treated probabilistically by considering the integration error as a random variable, and we show how the corresponding probabilities can be calculated. Handling the integration error as a random variable allows us to evaluate the accuracy of integration on very coarse grids where asymptotic error estimates cannot be applied.

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“…Numerous examples include acoustics and signal processing [1,2], image reconstruction [3], microbiology [4], ecological applications [5], …”

Section: Introductionmentioning

confidence: 99%

Evaluation of peak functions on ultra-coarse grids

Petrovskaya

Embleton

2013

Proc. R. Soc. A.

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“…Due to the inherent frequency response characteristics of the various electrical and mechanical components of the system depicted in Figure 1 (Kaczka and Lutchen, 2004), the resulting oscillatory V̇ , volume, and P tr signals yielded amplitude spectra which were non-uniform (Figure 2). Phase distortions between A/D channels resulting from multiplexer delays were corrected in real-time using a third-order Lagrange polynomial interpolation technique (Barwicz et al, 1989; Yaroslavsky et al, 2005). Between oscillatory pressure excitations, each dog was reconnected to the conventional ventilator for a period of 4 to 5 minutes.…”

Section: Methodsmentioning

confidence: 99%

Constant-phase descriptions of canine lung, chest wall, and total respiratory system viscoelasticity: Effects of distending pressure

Kaczka

Smallwood

2012

Respiratory Physiology & Neurobiology

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The dynamic mechanical properties of the respiratory system reflect the ensemble behavior of its constituent structural elements. This study assessed the appropriateness of constant-phase descriptions of respiratory tissue viscoelasticity at various distending pressures. We measured the mechanical input impedance (Z) of the lungs, chest wall and total respiratory system in twelve dogs at mean airway pressures from 5 to 30 cmH2O. Each Z was fitted with a constant-phase model which provided estimates tissue damping (G), elastance (H), and hysteresivity (η = G/H). Both G and H sharply increased with increasing distending pressure for the lungs and chest wall, while η attained a minimum near 15-20 cm H2O. Model fitting errors for the lungs and total respiratory system increased for distending pressures greater than 20 cm H2O, indicating that constant-phase descriptions of parenchymal and respiratory system viscoelasticty may be inappropriate at volumes closer to total lung capacity. Such behavior may reflect alterations in load distribution across various parenchymal stress-bearing elements.

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“…The particularities of the numerical methods used also make some differences in the integration and in the Fourier transform (Yaroslavsky et al, 2005).…”

Section: Slopes and Heights Sd Valuesmentioning

confidence: 99%

DABAM: an open-source database of X-ray mirrors metrology

Río

Bianchi

Cocco

et al. 2016

J Synchrotron Radiat

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An open-source database containing metrology data for X-ray mirrors is presented. It makes available metrology data (mirror heights and slopes profiles) that can be used with simulation tools for calculating the effects of optical surface errors in the performances of an optical instrument, such as a synchrotron beamline. A typical case is the degradation of the intensity profile at the focal position in a beamline due to mirror surface errors. This database for metrology (DABAM) aims to provide to the users of simulation tools the data of real mirrors. The data included in the database are described in this paper, with details of how the mirror parameters are stored. An accompanying software is provided to allow simple access and processing of these data, calculate the most usual statistical parameters, and also include the option of creating input files for most used simulation codes. Some optics simulations are presented and discussed to illustrate the real use of the profiles from the database.

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Frequency responses and resolving power of numerical integration of sampled data

Cited by 22 publications

References 12 publications

Evaluation of peak functions on ultra-coarse grids

Evaluation of peak functions on ultra-coarse grids

Constant-phase descriptions of canine lung, chest wall, and total respiratory system viscoelasticity: Effects of distending pressure

DABAM: an open-source database of X-ray mirrors metrology

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