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Statistical Interpolation of Non-Gaussian AR Stochastic Processes

Barzegar Khalilsarai, Mahdi | 2015

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 47538 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Amini, Arash
  7. Abstract:
  8. white noise or an innovation process through an all-pole filter. Applications of these processes include speech processing, RADAR signals and stock market data modeling. There exists an extensive research material on the AR processes with Gaussian innovation, however studies about the non-Gaussian case have been much more limited, while in many applications the asymptotic behavior of the signal is non-Gaussian. Non-Gaussian processes have an advantage over Gaussian ones in being capable of modeling sparsity. Assuming an appropriate non-Gaussian innovation one can suggest a more realistic description of sparse signals and predict their behavior or estimate their unknown values successfully. Due to the physical limitations in processing continuous domain signals, we always have access to only a set of samples, while in many cases an estimation of signal values in points other than the sampling instants is needed. The act of estimating signal values in non-sampling instants is called interpolation. Classic theorems of sampling, provide the necessary and sufficient conditions for band-limited signals and processes to be recovered from their samples. However, these theorems can not be applied to AR processes, since they are not band-limited. Instead, statistical properties of the process can play a similar role in employing the interpolation procedure. In the Gaussian scenario, linear estimators are optimal in terms of mean squared error. But, unfortunately the tools used in the Gaussian case do not apply to non-Gaussian processes and the optimal interpolator is generally non-linear for them. This thesis is dedicated to introducing a novel non-Gaussian innovation model with an AR process of order 1. It also provides the optimal interpolator for the final AR(1) process with regard to the mean squared error (MSE) criterion. It will be shown that the proposed model and its interpolation method are superior compared to the classical Gaussian regime
  9. Keywords:
  10. Interpolation ; Innovation ; Sparse Signal Processing ; Mean Square Error (MSE) ; Non-Gaussian Autoregressive Processes ; Optimal Estimator

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