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In the thesis, we study the data collected from twelve-note music of Webern and Schoenberg, including opus 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 and opus 31 of Webern and opus 25, 33a and opus 37 of Schoenberg. The data consists of the following two kinds. The data of the first kind consists of the four basic forms of the twelve-tone music. And the data of the second kind consists of the twelve-tone derived from the matrix of the twelve-note music. We will introduce the twelve-note music first and then study two main topics about twelve-note music in this thesis. In the first part, we consider the Markov properties of the first kind data. We compare the sample autocorrelation function and autocorrelation function of the fitted model to determine the fitness of the Markovian model. In the second part, we build the time series model for the second kind data. Sample autocorrelation function¡Bpartial autocorrelation function and extended autocorrelation function are used to determine the orders of the models. The best model is selected based on the AICC. Finally, we check the fitness of the models using sample autocorrelation function and partial autocorrelation function of the residuals.

In order to account for spatial correlation in residuals in regression models for areal and lattice data, different disciplines have developed distinct approaches. Bayesian spatial statistics typically has used a Gaussian conditional autoregressive (CAR) prior on random effects, while geographers utilize Moran's I statistic as a measure of spatial autocorrelation and the basis for creating spatial models. Recent work in both fields has recognized and built on a common feature of the two approaches, specifically the implicit or explicit incorporation into the linear predictor of eigenvectors of a matrix representing the spatial neighborhood structure. The inclusion of appropriate choices of these vectors effectively reduces the spatial autocorrelation found in the residuals. We begin with extensive simulation studies to compare Bayesian CAR models, Restricted Spatial Regression (RSR), Bayesian Spatial Filtering (BSF), and Eigenvector Spatial Filtering (ESF) with respect to estimation of fixed-effect coefficients, prediction, and reduction of residual spatial autocorrelation. The latter three models incorporate the neighborhood structure of the data through the eigenvectors of a Moran operator. We propose an alternative selection algorithm for all candidate predictors that avoids the ad hoc approach of RSR and selects on both model fit and reduction of autocorrelation in the residuals. The algorithm depends on the marginal posterior density a quantity that measures what proportion of the total variance can be explained by the measurement error. The algorithm selects candidate predictors that lead to a high probability that this quantity is large in addition to having large marginal posterior inclusion probabilities (PIP) according to model fit. Two methods were constructed. The first is based on orthogonalizing all of the candidate predictors while the second can be applied to the design matrix of candidate predictors without orthogonalization. Our algorithm was applied to the same simulated data that compared the RSR, BSF and ESF models. Although our algorithm performs similarly to the established methods, the first of our selection methods shows an improvement in execution time. In addition, our approach is a statistically sound, fully Bayesian method.

OFDM is a fast growing technology in the area of wireless communication due to its numerous advantages and applications. The current and future technologies in the area of wireless communications like WiMAX, WiFi, LTE, MBWA and DVB-T uses the OFDM signals. The OFDM technology is applicable to the radio communication as well as the acoustic communication. Though the licensed spectrum is intended to be used only by the spectrum owners, Cognitive radio is a concept of reusing this licensed spectrum in an unlicensed manner. Cognitive radio is motivated by the measurements of spectrum utilization . Cognitive radio must be able to detect very weak primary users signal and to keep the interference level at a maximum acceptable level. Hence spectrum sensing is an essential part of the cognitive radio. Spectrum is a scarce resource and spectrum sensing is the process of identifying the unused spectrum, without causing any harm to the existing primary user’s signal. The unused spectrum is referred to as spectrum hole or white space and this spectrum hole could be reused by the cognitive radio. This thesis work focuses on implementing primary acoustic transmitter to transmit the OFDM signals from a computer through loudspeaker and receive the signals through a microphone. Then by applying different detection methods on the received OFDM signal for detection of the spectrum hole, the performance of these detection methods is compared here. The commonly used detection methods are power spectrum estimation, energy detection and second–order statistics (GLRT approach, Autocorrelation Function (ACF) detection and cyclostationary feature detection ). The detector based on GLRT approach exploits the structure of the OFDM signal by using the second order statistics of the received data. The thesis mainly focuses on GLRT approach and ACF detectors and compare their performance.

It¡¦s not easy to keep photographs clean in every day. A photograph is liable to be polluted by accumulating defects such as dusts, which can degrade the imaging quality. In the thesis, a method of image restoration is proposed for image polluted by multiplicative transmittance noise. The method is based on estimating the approximate autocorrelation function of the unpolluted image. This autocorrelation function is obtained by analyzing the relationship among the autocorrelation function for polluted image, unpolluted image and noise. Further more, the noisy image is restored by the property of the autocorrelation function. A polluted photograph in imaging system is modeled by a thin random screen against the original image. In this model, defects are Poisson-distribution and may be overlapped. Since transmittance effect of each defect is multiplicative, the transmittance of random screen is computed as a product of Poisson-distribution-centered random function. Then, the statistical autocorrelation function of random screen is accordingly computed. More specifically, we should rearrange image data as periodic signal to avoid insufficient data in computing the process autocorrelation function. The simulated polluted image is restored by the amplitude information from the estimated autocorrelation function of the original image. Simulating results is demonstrated that the RMS of the restored image computed with the polluted image is improved.

No description available.

Thesis (Ph. D.)--Ohio State University, 2007. / Full text release at OhioLINK's ETD Center delayed at author's request

Thesis (Ph.D.)--Baylor University, 2008. / Includes bibliographical references (p. 263-269).

Thesis (M.S.)--Ohio University, November, 1996. / Title from PDF t.p.

Thesis (Ph. D.)--Oregon State University, 2010. / Printout. Includes bibliographical references (leaves 113-123). Also available on the World Wide Web.