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

本研究解决一维准一元滤波器组的编码增益优化问题。作为极端特例，准酉滤波器组包括子带编码器和变换编码器，在没有量化的情况下具有完美的信号恢复优势。这种方法在信号处理和系统理论中开辟了一大类问题，其中一些是基本的，所有这些问题都得到了解决。滤波器组变压器的一些特性与传统的傅立叶变换特性（如卷积定理）相似，这些特性也得到了解决。再一次，编码增益优化的准正卷积和标准正交卷积被解决。上述研究也被推广到非均匀滤波器组（即具有不等抽取比的系统，如最常见的离散时间小波变压器）。最后，将这些思想扩展到多维多速率系统。

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.