CAREER: Wavelet-Based Nonlinear Digital Signal Processing

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The application of Digital Signal Processing (DSP) has been driven by the rapid growth of digital computing power and the need for fast, reliable computer processing techniques for communication, biomedical, manufacturing, seismic, radar, and a wide variety of other signals for commercial and scientific interest. Despite the great success of traditional DSP techniques, many real- world problems remain unsolved due to the nonlinearities and non-Gaussian noises often encountered in these applications. Solving these more complex problems requires the development of new, more flexible, nonlinear DSP theory and tools. The objectives of this project are to develop these new tools and theory, and to transfer them directly into practice and into the engineering classroom. A new framework for nonlinear DSP based on the wavelet transform is currently under study. The desirable properties of the wavelet transform, such as time- frequency localization and signal compression, are being exploited to develop sophisticated, yet tractable, nonlinear processing techniques. Key elements of the work include the development of statistical re-sampling methods and data- adaptive wavelet analyses for nonlinear DSP. Applications of the new framework to cross-disciplinary problems in imaging and communications are being investigated. The principal investigator is concurrently developing innovative approaches to engineering education including Internet-based tutorials and documentation of new research, cross-disciplinary student design projects, and tools for curriculum assessment.