計畫名稱：一系列三維二次曲面數位濾波器之設計與應用
執行起迄：2012/08/01~2013/07/31
總核定金額：623,000元
中文摘要：在本計畫中，我們致力於一系列三維FIR二次曲面數位濾波器之設計及其應用之研究。在本計畫中，我們將該類濾波器定義為通帶截止頻率曲面為二次曲面之三維數位濾波器。一般而言，二次曲面概分為橢球面、單葉雙曲面、雙葉雙曲面、橢形錐面、橢圓拋物面、雙曲拋物面等六大類。由於數位濾波器之頻率響應具週期性，故本計畫中我們僅探討橢球面濾波器、單葉雙曲面濾波器、雙葉雙曲面濾波器、橢形錐面濾波器之設計及其應用，另具任意傾斜角度之橢球面濾波器亦在探討之列。 在現有文獻中，除了圓形錐面濾波器較被廣泛探討外，極少文獻涉及二次曲面數位濾波器之設計及其應用之研究。本計畫之動機是基於圓形錐面濾波器廣泛應用於地質學、地震學、聲納及雷達工程等，因此我們相信二次曲面數位濾波器在醫學工程及上述領域當有更廣泛潛在之應用，值得深入探討。 在本計畫中，我們採用McClellan轉換法來設計三維FIR二次曲面數位濾波器。為了避免超量問題(scaling problem)的發生，在設計過程中，我們加入了一些限制條件。這些限制條件分為顯性限制條件及隱性限制條件，前者可用來推導出係數之間的關係，簡化系統之設計；後者我們以反覆拉氏逼近法(iterative Lagrange multiplier approach)來決定。 本計畫另一目標為擴展上述方法至可調式二次曲面數位濾波器之設計。此類濾波器之優點為透過改變一個或數個可調之參數即可調整二次曲面數位濾波器之頻率響應，毋須重新設計一個新的系統。
英文摘要：In this project, the design and applications of a class of 3-D FIR quadric filters is investigated. It is noted that quadric filters belong to a branch of digital filters, whose passband edges are of the forms of quadric surfaces. Generally, there are six basic types of quadric surface: ellipsoid, hyperboloid of one sheet, hyperboloid of two sheets, elliptic cone, elliptic paraboloid, and hyperbolic paraboloid. Due to the periodicity of frequency response for digital filters, only design of ellipsoid filter, hyperboloid filter of one sheet, hyperboloid filter of two sheets, and elliptic cone filter will be proposed, and the extension to ellipsoid filter with arbitrary inclinations will also be presented. In the existing literature, there are seldom works that concern the so called “quadric filter” except the circular cone filter, and the motivation for this proposal is based on the wide applications of circular cone filters in areas such as processing of geological and seismological data, sonar and radar engineering, and motion discrimination. It is believed that there must be more applications for quadric filters such as in biomedical engineering, and the fields stated above, which makes this project more valuable to be deeply probed. For the design of 3-D FIR quadric filters, the technique of McClellan transformation will be applied. To avoiding occurrence of scaling problem, some constraints are incorporated into the design formulation, which are classified into explicit constraints and implicit constraints. The former will lead to the relationship of subfilter coefficients, and the latter will be determined by the iterative Lagrange multiplier approach. Moreover, there is another trend of filter design concerning the design of variable filters which are applied applications where the frequency characteristics need to be adjustable. In this project, it will be dealt with for the design of variable 3-D FIR quadric filters by McClellan transformation and the iterative Lagrange multiplier approach, too.