The research component of this faculty early career development proposal is aimed at developing a large, important, and fundamentally new class of multirate filter banks, systems and wavelets. Traditional developments of this topic within the signal processing community have been strongly motivated by applications involving signal analysis. In strong contrast, the research in this proposal is motivated by some important contemporary applications involving signal synthesis. In particular, multirate filterbank theory, wavelet theory have a potentially important and largely unexplored role to play in the synthesis of waveforms for a wide variety of broadband communications and remove sensing applications. In these applications, fundamentally different types of design criteria and constraints come into play in developing suitable multirate structures. Foremost among the important differences is that while for most applications involving signal analysis strong localization in time and frequency is emphasized, the kinds of applications that will be the focus of this work will require filterbanks and wavelets whose energy is widely dispersed in both time and frequency. We propose to explore several classes of orthogonal and biorthogonal dispersive, "pseudorandom" filterbanks and wavelet bases. Several specific application areas are to be pursued under the proposed research. One that will be emphasized will be digital wireless communications. Here dispersive filterbanks and wavelets are expected to lead to new code-division multiplexing systems that more efficiently combat fading, jamming, and other forms of multiple-access interference. Furthermore, we plan to implement the new wireless modems we develop in a DSP-based, real-time 900 Mz indoor wireless system testbed recently developed by the principal investigator as part of his wireless communications laboratory. The educational component of the proposal encompasses significant curriculum development at b oth the undergraduate and graduate levels, and a strong investment in the mentoring of graduate students. One teaching initiative involves the development of a recently introduced unified new undergraduate subject. This subject introduces undergraduate students, for the first time, to the fundamentals of communications, control and signal processing from a common perspective and which builds on a foundation of basic signals, systems, and probability. The second major teaching initiative involves the re-engineering of the fundamental graduate subject on stochastic processes, detection and estimation at MIT. In this subject, the object is to redevelop a syllabus, course notes, Matlab computer exercises, and homework problems that emphasize modern, unified perspective to random and deterministic signals and the associated signal processing algorithms. These curricular changes will also allow a number of advanced topics, including multiscale and nonlinear signal processing, to be incorporated. A final component of the education plan involves continued active mentoring of a diverse group of graduate students and nurturing their intellectual, professional, and personal growth. Ultimately, of course, this interaction is one of the most gratifying and important aspects of a academic career.
