A Simulation and Theoretical Analysis of the Doubly Stochastic Homodyne K Scattering Model
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| Title: | A Simulation and Theoretical Analysis of the Doubly Stochastic Homodyne K Scattering Model |
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| Authors: | Gatt, Philip |
| Committee Members: | Phillips, Ronald |
| Summary: | A theoretical analysis and computer simulation of the Homodyne K (HK) scattering model was performed. Several mathematical descriptions of the probability density function (PDF) were derived, along with numerical methods for computing the HK PDF. The theoretical analysis showed that, except for special cases, no general tractable solution to the HK PDF seemed to exist; however, accurate PDFs could be generated numerically. HK parameter estimation methods were also developed, and it was shown that these parameters are highly sensitive to the statistical moments of the data. The computer simulation of the HK process verified the theoretical analysis, which describes the interrelationship between the model parameters, the moments, the PDF and power spectral density (PSD) of the process. A byproduct of the computer simulation was the development of an efficient algorithm for the simulation of a correlated low pass approximate gamma process. Many computer tools were also developed including high speed statistical analysis algorithms and special function subroutines. |
| URL: | https://stars.library.ucf.edu/rtd/4140 |
| Database: | OpenDissertations |
| Abstract: | A theoretical analysis and computer simulation of the Homodyne K (HK) scattering model was performed. Several mathematical descriptions of the probability density function (PDF) were derived, along with numerical methods for computing the HK PDF. The theoretical analysis showed that, except for special cases, no general tractable solution to the HK PDF seemed to exist; however, accurate PDFs could be generated numerically. HK parameter estimation methods were also developed, and it was shown that these parameters are highly sensitive to the statistical moments of the data. The computer simulation of the HK process verified the theoretical analysis, which describes the interrelationship between the model parameters, the moments, the PDF and power spectral density (PSD) of the process. A byproduct of the computer simulation was the development of an efficient algorithm for the simulation of a correlated low pass approximate gamma process. Many computer tools were also developed including high speed statistical analysis algorithms and special function subroutines. |
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