Optimal Filtering Applied to the Inversion of the Laplace Transform
The laser scattering measurement of the Brownian motion of particles suspended in a colloid may be modeled by the integral equation
which is the Laplace transform. In this equation g(t) is the autocorrelation of the electric field of scattered light, and G(γ) the linewidth distribution describing the particle size distribution of the colloid, with the property G(γ)≥0 for all γ.
KeywordsStatistical Noise Laplace Transform Noise Spectrum Optimal Filter Infinite Variance
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Unable to display preview. Download preview PDF.
- 1.Johnson, R.P.C. and Ross, D.A., Analysis of Organic and Biological Surfaces. Edited by P. Echlin, Chapter 20: Laser Doppler Microscopy and Fiber Optic Doppler Anemometry, 507-527, John Wiley and Sons (1984).Google Scholar
- 2.Ross, D.A. “Laser Particle Sizing by Orthogonal Polynomial,” Proceedings of the Fourth International Conference on Photon Correlation Techniques in Fluid Mechanics, 15 (1980).Google Scholar
- 6.Bertero, M., Boccacci, P and Pike E.R., “On the recovery and resolution of exponential relaxation rates from exponential data: a singularvalue analysis of the Laplace transform inversion in the presence of noise.” Proc. R. Soc. London Ser. A (GB), 383, 1784, 15–29 (1982).zbMATHCrossRefGoogle Scholar
- 8.Norbert Wiener, Extrapolation, interpolation, and smoothing of stationary time series, with engineering applications, Technology Press of MIT (1949).Google Scholar
- 9.R.E. Kaiman, “A new Approach to Linear Filtering and Prediction Problems,” ASME Transactions, 82D (1960).Google Scholar
- 10.R.E. Kaiman and R.C. Bucy, “New Results in Linear Filtering and Prediction Theory,” ASME Transactions, 83D (1961).Google Scholar
- 11.Handbook of Mathematical Functions, Edited by M. Abramowitz and I.E. Stegun, National Bureau of Standards, Tenth Printing (1972).Google Scholar
- 12.Papoulus, A., Probability. Random Variable, and Stochastic Processes, First Eddition, McGraw-Hill, Inc. (1965).Google Scholar
© Springer Science+Business Media New York 1988