Erdol, Nurgun

In this paper we propose using parametric modeling by employing a Multi-Pulse Excited Linear Predictive Coded (MPE-LPC) filter to synthesize the guitar. First we introduce different methods for sound synthesis. A detailed discussion including the derivation of LPC and MPE presented. Then we study the impulse and steady state response of the guitar signal. An implementation of the MPE-LPC method to model the guitar is covered in detail and opportunities to improve the compression ratio are discussed. We then present simulation results with a set of fixed parameters, which are used as a benchmark to observe performance trade-offs by varying the model parameters to improve the compression ratio. Finally, we discuss limitations of the modeling algorithm for use with wide-band transient musical sounds and possible applications of the MPE-LPC model as a method to dynamically calculate samples for use with wavetable synthesis of steady state sounds.

This thesis provides detailed analysis and design techniques for Wigner-Ville spectrum (WVS) estimators for use with cyclostationary signals. The resulting class of estimators represent a newly defined subset of Cohen's class characterized by a mixed discrete-time/continuous-frequency smoothing kernel. Although both time-variant and shift invariant versions of the estimator are developed, emphasis is placed on the shift-invariant version which is designed to estimate the WVS over an entire period from a single observation. Bias and variance expressions are derived for the new estimator, and these are compared with the general estimator. For this development, we also derive mean and covariance expressions for the general quasi-stationary based estimators, both for the autocorrelation estimator and for the WVS estimator. The concept of quasi-stationarity is extended to cyclostationary models, and we develop a novel measure of kernel smoothing and variance reduction termed the time-bandwidth area. This is a generalization of time-bandwidth product to describe arbitrary kernel functions, even those which are not governed by the uncertainty principle (such as the newly proposed estimators). The properties of the estimator are examined in terms of constraints on the smoothing kernel. In sharp contrast to the conventional estimators based on the quasi-stationary assumption, the low bias and low variance constraints for the new class of estimators do not contradict one another. The relationship between time dependent spectral estimation for nonstationary processes and classical Blackman-Tukey type spectral estimation for stationary processes is developed next. Using examples the utility of the new estimator kernels are shown. It is seen that in random or noisy environments it may be difficult to achieve a reasonable trade-off between variance reduction and bias using conventional estimators. In the examples any assumption of quasi-stationarity sufficient to produce a low variance estimate would destroy many or all of the nonstationary features of the signal. However, since the signals are cyclostationary we can employ the new class of estimators to achieve an excellent balance between bias and variance reduction.

The cochlea provides frequency selectivity for acoustic input signal processing in mammals. The excellent performance of human hearing for speech processing leads to examination of the cochlea as a paradigm for signal processing. The components of the hearing process are examined and suitable models are selected for each component's function. The signal processing function is simulated by a computer program and the ensemble is examined for behavior and improvement. The models reveal that the motion of the basilar membrane provides a very selective low pass transmission characteristic. Narrowband frequency resolution is obtained from the motion by computation of spatial differences in the magnitude of the motion as energy propagates along the membrane. Basilar membrane motion is simulated using the integrable model of M. R. Schroeder, but the paradigm is useful for any model that exhibits similar high selectivity. Support is shown for an hypothesis that good frequency discrimination is possible without highly resonant structure. The nonlinear magnitude calculation is performed on signals developed without highly resonant structure, and differences in those magnitudes are signals shown to have good narrowband selectivity. Simultaneously, good transient behavior is preserved due to the avoidance of highly resonant structure. The cochlear paradigm is shown to provide a power spectrum with serendipitous good frequency selectivity and good transient response simultaneously.

A measure of the potential of a receiver for detection is detectability. Detectability is a function of the signal and noise, and given any one of them the detectability is fixed. In addition, complete transforms of the signal and noise cannot change detectability. Throughout this work we show that "Subspace methods" as defined here can improve detectability in specific subspaces, resulting in improved Receiver Operating Curves (ROC) and thus better detection in arbitrary noise environments. Our method is tested and verified on various signals and noises, both simulated and real. The optimum detection of signals in noise requires the computation of noise eigenvalues and vectors (EVD). This process neither is a trivial one nor is it computationally cheap, especially for non-stationary noise and can result in numerical instabilities when the covariance matrix is large. This work addresses this problem and provides solutions that take advantage of the subspace structure through plane rotations to improve on existing algorithms for EVD by improving their convergence rate and reducing their computational expense for given thresholds.