A Model Matching Approach to Multirate System Design

多速率数字系统在通信和信号处理中有重要的应用，包括重采样、内插、窄带滤波、传真系统、子带编码、多路转换、多分辨率分析和小波。这项研究正在开发基于模型匹配方法的多速率信号处理系统的系统设计算法，其中理想系统(模型)由实际的多速率系统近似，该多速率系统由数字滤波器、调制器和上采样器/下采样器等部件组成。问题是如何选择实际系统的参数，使系统的性能尽可能接近理想系统。本研究中使用的系统之间的差异的测量是基于两个系统对所有可能的投入的输出的差异。对于所有有界能量输入信号，选择系统参数以最小化输出信号之间的差值的最大能量。这种误差度量提供了这样的系统，其中近似的质量对系统的特定类型的输入不敏感。在直观设计方法有限的复杂系统中，例如在级联多速率系统的设计中，预计会比传统设计有最显著的改进。

Multirate digital systems have important applications in communication and signal processing including resampling, interpolation, narrow band filtering, fax systems, subband coding, transmultiplexing, multiresolution analysis, and waveletts. This research is developing algorithms for the systematic design of multirate signal processing systems based on a model-matching approach where an ideal system (model) is approximated by a practical multirate system consisting of components such as digital filters, modulators, and upsamplers/downsamplers. The problem is to choose the parameters of the practical system so that the performance of the system is as close as possible to the ideal system. The measurement of the difference between systems used in this research is based on the difference in outputs of the two systems for all possible inputs. System parameters are chosen to minimize the maximum energy of the difference between output signals for all bounded energy input signals. This error measure gives systems where the quality of the approximation is insensitive to the particular type of input to the system. The most significant improvements over conventional designs are expected in complicated systems where intuitive design methods are limited, such as in the design of cascaded multirate systems.