管線化遞迴性濾波器設計之研究

Abstract

在遞迴性濾波器的設計中，相鄰輸出之間的依賴性妨礙了濾波器本身被 管線化的能力。這個限制可以利用前瞻計算的技術加以打破，從而設計出 兩種不同的管線化遞迴性濾波器：散佈型和聚集型。在本文中，我們討論 了兩者在硬體實現上的問題以及散佈型管線化遞迴性濾波器在合成上的問 題。傳統上，散佈型管線化遞迴性濾波器是利用極點零點對消法或非線性 規畫法來加以合成的。第一種方法所合成的濾波器具有多組互相抵消的極 點與零點，這些極點與零點會影響到濾波器的係數量化效應。我們利用極 點與零點移動量的計算來描述這項影響，得到一個非常簡單，但是與實際 結果相當吻合的模型。另外，我們提出了兩種新的方法來合成散佈型管線 化遞迴性濾波器。它們都採用了直接合成的觀念，同時也都只需要線性的 計算量。所設計出來的濾波器對硬體的需求可以減少。我們利用二階管線 化心縮式陣列作為遞迴性濾波器的硬體實現。前瞻計算所提供的平行度與 管線化結構所提供的平行度在設計過程中被同時得考慮，兩者互相匹配， 從而獲得最高速的硬體實現。 The tight dependence between successive outputs limits the recursive filter to be pipelined. This restriction can be released by the look-ahead technique. Two kinds of pipelined recursive filters can then be designed. One is the scattered form, and the other is the clustered form. In this thesis, we study their implementation problems and the synthesis issues of the scattered one. The pipelined recursive filters of scattered scheme are generally synthesized by the pole-zero cancellation technique or nonlinear programming. The former makes the filter have many cancelling pole and zero pairs that will alter the coefficient quantization effects. We use the calculations of the pole and zero movements to describe this influence. The analysis model is simple and very coincident with real simulation. Besides, we propose two new methods to synthesize the pipelined recursive filters of scattered scheme. The direct synthesis concept and the linear computation load are the common features. The designed filter could have fewer hardware cost. Two-level pipelined systolic arrays are dedicated to implement the pipelined recursive filters. We consider the parallelisms that are provided by the look-ahead algorithm and by the pipelined structure at the same time. A systematic method is derived to match them well and have implementations of the highest speed.