## Wavelet Filter Banks in Perceptual Audio Coding

This thesis studies the application of the wavelet filter bank (WFB) in perceptual audio coding by providing brief overviews of perceptual coding, psychoacoustics, wavelet theory, and existing wavelet coding algorithms. Furthermore, it describes the poor frequency localization property of the WFB and explores one filter design method, in particular, for improving channel separation between the wavelet bands. A wavelet audio coder has also been developed by the author to test the new filters. Preliminary tests indicate that the new filters provide some improvement over other wavelet filters when coding audio signals that are stationary-like and contain only a few harmonic components, and similar results for other types of audio signals that contain many spectral and temporal components. It has been found that the WFB provides a flexible decomposition scheme through the choice of the tree structure and basis filter, but at the cost of poor localization properties. This flexibility can be a benefit in the context of audio coding but the poor localization properties represent a drawback. Determining ways to fully utilize this flexibility, while minimizing the effects of poor time-frequency localization, is an area that is still very much open for research.

## Real-time Motion Picture Restoration

Through age or misuse, motion picture films can develop damage in the form of dirt or scratches which detract from the quality of the film. Removal of these artifacts is a worthwhile process as it makes the films more visually attractive and extends the life of the material. In this thesis, various methods for detecting and concealing the effects of film damage are described. Appropriate algorithms are selected for implementation of a system, based on a TMS320C80 video processor, which can remove the effects of film defects using digital processing. The restoration process operates in real-time at video frame rates (30 frames per second). Details of the software implementation of this system are presented along with results from processing damaged film material. The effects of damage are significantly reduced after processing.

## Least Squares and Adaptive Multirate Filtering

This thesis addresses the problem of estimating a random process from two observed signals sampled at different rates. The case where the low–rate observation has a higher signal–to– noise ratio than the high–rate observation is addressed. Both adaptive and non–adaptive filtering techniques are explored. For the non–adaptive case, a multirate version of the Wiener–Hopf optimal filter is used for estimation. Three forms of the filter are described. It is shown that using both observations with this filter achieves a lower mean–squared error than using either sequence alone. Furthermore, the amount of training data to solve for the filter weights is comparable to that needed when using either sequence alone. For the adaptive case, a multirate version of the LMS adaptive algorithm is developed. Both narrowband and broadband interference are removed using the algorithm in an adaptive noise cancellation scheme. The ability to remove interference at the high rate using observations taken at the low rate without the high–rate observations is demonstrated.

## A DSP-Based Computational Engine For a Brain-Machine Interface

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The fields of neurobiology and electrical engineering have come together to pursue an integrated Brain-Machine Interface (BMI). Signal processing methods are used to find mapping algorithms between motor cortex neural firing rate and hand position. This cognitive extension could help patients with quadriplegia regain some independence using a thought-controlled robot arm. Current signal processing methods to achieve realtime neural-to-motor translation involve large, multi-processor systems to produce motor control parameters. Eventually, software running in a portable signal processing system is needed to allow for the patient to have the BMI in a backpack or attached to a wheelchair. This thesis presents a DSP-Based Computational Engine for a Brain-Machine Interface. The development of a DSP Board based on the Texas Instruments TMS320VC33 DSP will be presented, along with implementations of two digital filters and their training methods: 1) FIR trained with Normalized Least Mean Square Adaptive Filter (NLMS) and 2) Recurrent Multi-Layer Perceptron (RMLP) trained with Real-Time Recurrent Learning (RTRL). The requirements of the DSP Board, component selection and integration, and control software are discussed. The DSP implementations of the digital filters are presented, along with performance and timing analysis in real data collected from an Owl Monkey at Duke University. The weights of the FIR-NLMS filter converged similarly on the DSP as they did in MATLAB. Likewise, the weights of the RMLP-RTRL filter converged similarly on the DSP as they did using the Backpropagation Through Time method in NeuroSolutions. The custom DSP Board and two digital algorithms implemented in this thesis create a starting point for an integrated, portable, real-time signal processing solution for a Brain-Machine Interface.

## Orthogonal Adaptive Digital Filters with Applications to Acoustic System Identification

The Transform-Domain LMS Algorithm (Narayan, 1983) is studied in the context of an acoustic system identification problem. The power estimator in this two-stage digital filter is shown to affect the achievable rates and depths of convergence significantly. Preferred values for the two tracking parameters, $\beta$ and $\mu,$ are determined. Dynamic Step-size Initialization is proposed to improve early convergence by accelerating the rate at which true power measurements replace (arbitrary) initial values. Later, linear estimators are shown to be sub-optimal, particularly where the spectral distribution of the reference changes rapidly. A simple non-linear Peak Window Power Estimator which eliminates these problems is described. It will be shown to improve the tracking rates and misadjustment simultaneously. The benefits of these methods are demonstrated using FIR sequences representative of typical acoustic environments and using recordings from a commercial telephone set. The proposed structures surpass theexisting algorithms consistently under all circumstances tested.