The proposed project is focused on the theory, structure and design methods for the perfect-reconstruction (PR) /ncar-perfect- reconstruction (NPR) filter banks and their applications in signal conversion, detection and adaptation. High performance filter banks with high attenuation are needed in many applications such as audio compression algorithms, high-bandwith high-resolution A/D converters, wideband signal detection systems and adaptive filtering algorithms. The design of these filter banks are very difficult because of the nonlinear relations between the parameters and the objective function. New structures and design methods will be investigated. They will open up new classes of filter banks, some of which are addressed in the project. They are the biorthogonal cosine-modulated filter bank, the infinite-impulse- response (IIR) cosine-modulated filter bank, and the nonuniform filter bank. These filter banks will be used in several applications such as high-performance A/D converter, nondestructive evaluation, echo cancellation and adaptive noise cancellation systems. The education part consists of writing an undergraduate textbook on the theory and design methods of filter bank wavelets, establishing an internet site for the storage of design programs and coefficients of filter banks and developing a new course on time- frequency and time-scale analysis.
