多項式速率轉換濾波器之最佳設計

Abstract

在數位訊號處理中，速率轉換是頻繁地被拿來應用，速率轉換包含著插值器、低通濾波器和抽值器這三個元件。如果一個系統需要應用在不同的訊號處理速率下，則濾波器係數的儲存，必須使用一個大的記憶體空間去存放，對於這類問題，一般可使用多項式插值╱抽值濾波器。在這方法中，多項式函數是被使用去表示成一個規範型的類比濾波器的響應，對於所有的插值濾波器或抽值濾波器的設計，皆可藉由對此規範型類比濾波器做取樣的動作而完成。多項式濾波器的最大優點是在硬體上可有效地利用費洛結構實現，對於多項式濾波器的現存設計方式大部分都只考慮在如何去近似一個理想的低通濾波器，或者是如何去處理分數延遲的問題。在插值和抽值的處理中，都沒有對頻譜特性去做ㄧ分析研究。故在本論文中，我們是對速率轉換濾波器做ㄧ個最佳化的設計，特別藉由頻譜的特性，使得設計出來的濾波器相對地會得到好的效能。

In signal processing, rate conversion is a frequently conducted operation. Rate conversion involves interpolation, filtering, and decimation. If a system has to operate in many different processing rates, many sets of filter coefficients have to be stored resulting in high memory requirement. A common remedy for this problem is to use polynomial-based interpolation/decimation filters. In this approach, polynomial functions are used to represent the response of an analog prototyping filter. All the required interpolation/decimation filters can then be obtained by sampling the prototyping filter. A distinct advantage of polynomial-based filters is that it can use the Farrow structure to implement the filtering operation efficiently. Existing design methods for the polynomial-based filters only consider how to approximate an ideal lowpass filter, or how to deal with the fractional delay problem. The spectrum integrality in the interpolation/decimation process has not been studied yet. In this thesis, we consider the optimum design of rate conversion filter. By specifically taking the spectrum property, we can obtain the corresponding filters with better performance.