New Techniques for Design and Implementation of One- Dimensional and Two-Dimensional Multirate Digital Filter Banks

本文的工作重点是研究多速率数字滤波器组系统在一维和二维信号处理中的应用。这些系统背后的基本原理是，如果一个离散时间信号被分成许多相邻的频带，那么每个频带中的信息可以单独编码。这通常会提高这些信号的存储/传输效率。改进的原因是，在判断每个子带所需精度的过程中，可以利用每个频段的特性（如平均能量，对人类感知的影响等）。通过这种方式，即使信号不受禁令限制，也可以通过简单地利用某些频段比其他频段更重要的事实来压缩信号。我们将努力设计和实现一组滤波器，这些滤波器将执行带分裂和重构。这是一个非常非常规的滤波器设计问题，因为使用非理想的带分裂滤波器和抽取器会产生混叠和其他类型的失真。因此，在设计和实现阶段需要更复杂的代数工具（如拟酉性和无损性）。除了在许多工程问题中的应用外，多速率滤波器组结构与信号采样、重构和块处理的基本原理密切相关。因此，对这一点的透彻理解将统一信号处理科学界感兴趣的几个方面。

The proposed effort is focused on study of multirate digital filter bank systems for application in one-dimensional and two-dimensional signal processing. The basic philosophy behind these systems is that if a discrete-time signal is split into a number of adjacent frequency bands, then the information in each of these bands can be coded separately. This often results in improved efficiency in storage/transmission of such signals. The improvement is a consequence of the fact that, the peculiarities of each frequency band (such as the average energy, the impact on human perception, etc.) can be exploited in the process of judging the precision required for each sub-band. In this way a signal can be compressed even if it is not ban-limited, simply by exploiting the fact that some frequency bands are more important than others. Effort will be directed towards the design and implementation of the set of filters which will perform the band-splitting and reconstruction. This is a very unconventional filter-design problem, because of aliasing and other types of distortions which result from the use of non-ideal band-splitting filters and decimators. Because of these, more complicated algebraic tools (such as paraunitariness and losslessness) are required in the design and implementation phase. In addition to its application in a number of engineering problems, the multirate filter bank structure is closely related to fundamentals of signal sampling, reconstruction, and block processing. A thorough understanding of this will therefore unify several aspects of interest to the signal- processing scientific community.