Uncertainties in Interpolated Spectral Data
نویسنده
چکیده
Interpolation is often used to improve the accuracy of integrals over spectral data convolved with various response functions or power distributions. Formulae are developed for propagation of uncertainties through the interpolation process, specifically for Lagrangian interpolation increasing a regular data set by factors of 5 and 2, and for cubic-spline interpolation. The interpolated data are correlated; these correlations must be considered when combining the interpolated values, as in integration. Examples are given using a common spectral integral in photometry. Correlation coefficients are developed for Lagrangian interpolation where the input data are uncorrelated. It is demonstrated that in practical cases, uncertainties for the integral formed using interpolated data can be reliably estimated using the original data.
منابع مشابه
Standard Addition Connected to Selective Zone Discovering for Quantification in the Unknown Mixtures
Univariate calibration method is a simple, cheap and easy to use procedure in analytical chemistry. A univariate analysis will be successful if a selective signal can be found for the analyte(s). In this work, two simple ways were used to find the selective signals, spectral ratio plot (SRP) and loading plot (LP). Both of them were able to discover the selective regions in the recorded data set...
متن کاملTarget Detection Improvements in Hyperspectral Images by Adjusting Band Weights and Identifying end-members in Feature Space Clusters
Spectral target detection could be regarded as one of the strategic applications of hyperspectral data analysis. The presence of targets in an area smaller than a pixel’s ground coverage has led to the development of spectral un-mixing methods to detect these types of targets. Usually, in the spectral un-mixing algorithms, the similar weights have been assumed for spectral bands. Howe...
متن کاملComparative Study of Exponential Signal by an Interpolated DFT Algorithm
In this paper, exponential signals in the frequency domain are accurately analyzed by an algorithm, and the peaks of the discrete Fourier transform (DFT) result are adopted to obtain parameters that include amplitudes, frequencies, damping, and phases. There are two steps for this algorithm: interpolated DFT and leakage elimination. Interpolated DFT refers to the three neighboring spectral line...
متن کاملInterference effects in short-term memory for timbre.
Four experiments investigated memory for timbre using the interpolated-tone paradigm [Deutsch, Science 168, 1604-1605 (1970)], in which participants discriminate pairs of tones (standard and comparison) separated by intervening (interpolated) tones. Interpolated tones varied from the standard tone in spectral similarity (within-dimensional variation), fundamental frequency (cross-dimensional va...
متن کاملInterpolation in Time Series: An Introductive Overview of Existing Methods, Their Performance Criteria and Uncertainty Assessment
A thorough review has been performed on interpolation methods to fill gaps in time-series, efficiency criteria, and uncertainty quantifications. On one hand, there are numerous available methods: interpolation, regression, autoregressive, machine learning methods, etc. On the other hand, there are many methods and criteria to estimate efficiencies of these methods, but uncertainties on the inte...
متن کامل