New Directions in One and Multidimensional Multirate Systems, Filter Banks, and Applications

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Vaidyanathan This research addresses coding gain optimization in one dimensional paraunitary filter banks. Paraunitary filter banks include both subband and transform coders as extreme special cases, and have the advantage of perfect signal recovery in the absence of quantization. This approach opens up a large class of problems, some fundamental, in signal processing and in systems theory, all of which are being addressed. A number of properties of the filter bank transformer that parallel traditional Fourier transform properties (e.g., the convolution theorem) are also being addressed. Again, the coding gain optimization for paraunitary and orthonormal convolvers is being addressed. The above research is also being generalized to nonuniform filter banks (i.e., systems with unequal decimation ratios, as in the most common discrete time wavelet transformers). Finally, several extensions of these ideas to multidimensional multirate systems are being considered.