基於晶格架構的數位全通濾波器與濾波器組之最佳化設計

Abstract

在數位訊號處理的參考文獻中，我們得知晶格架構有兩大優點：1 對於反射係數量化後所造成的誤差較小，亦即係數的敏感度較小。2 由於晶格架構是由許多單元串聯而成，而每個單元的內容相同，稱為模組，當需要更高階數的濾波器時，只需要增加串聯的模組，不需要重新設計電路，因此在積體電路的實現上有較方便的設計優點。 本論文著重在晶格架構與直接架構的設計比較。在一維部分，我們討論了數位全通濾波器、雙重互補濾波器對和正交鏡像濾波器組。在二維部分，我們討論了支持區間為非對稱半平面以及對稱半平面的全通濾波器，以及二維雙重互補濾波器對和二維正交鏡像濾波器組。本論文中有許多設計實例，呈現令人滿意的結果，因此可以驗證將晶格架構用在建構濾波器及濾波器組的可行性。

As we know from the apllications in digital signal processing, two merits about lattice structure are as follows. First, the sensitivity of quantization effets in the implementation of the system is smaller. Second, lattice structure is cascaded from many sections, which are called module. Each of them has the same contents. when it needs a filter with higher order, it only has to add modules to cascade, instead of redesign the circuit. Therefore, it is more convenient to accomplish the work of IC design. This thesis puts emphasis on the comparing the designs of lattice structure and direct form. In the part of 1-D case, we have discussed DAFs, DCFs, and QMF banks. In the part of 2-D case, we have discussed the NSHP and SHP DAFs, 2-D DCFs, and 2-D QMF banks. There are many examples in this thesis representing satisfactory results, so it can prove the feasibility of using lattice structure in the constructing of filters and filter banks.