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

本文的工作重点是多采样率数字滤波器组的研究 应用于一维和二维信号的系统 处理. 这些系统背后的基本理念是，如果 离散时间信号被分成多个相邻频带， 则这些频带中的每一个中的信息可以被单独编码。 这通常导致存储/传输的效率提高， 这样的信号。 这一改进是因为， 每个频带的特性（例如平均能量、 对人类感知的影响等）可以在这个过程中被利用 判断每个子带所需的精度。 通过这种方式， 即使没有禁令限制，也可以简单地通过利用 某些频段比其他频段更重要。 将努力设计和执行《原则和规则》， 将执行频带分离和重构的滤波器。 这是一个非常非传统的滤波器设计问题，因为混叠 和其他类型的失真，这是由于使用非理想的 带分离滤波器和抽取器。 由于这些，更多 复杂的代数工具（如仿酉性和无损性） 在设计和实施阶段需要。 除了其 在一些工程问题中的应用，多速率滤波器 存储体结构与信号采样的基本原理密切相关， 重建和块处理。 彻底了解这一点 因此，将统一信号的几个感兴趣的方面- 加工科学界。

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.