臺灣博碩士論文加值系統

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.

第一章 緒論 1
第二章 數位系統處理頻率轉換的方法 3
2-1 整數倍取樣頻率的轉換 3
2-1-1 升頻 ( Upsampling ) 3
2-1-2 降頻 ( Downsampling ) 7
2-2非整數倍取樣頻率的轉換實現方式 11
第三章 內插函數 12
3-1 線性內插 ( Linear Interpolation ) 12
3-2 立方B-樣條內插法( Cubic B-Spline Interpolation ) 13
3-3 正弦內插函數 ( Sinc Interpolation ) 16
3-4 立方迴旋內插函數( Cubic Convolution Interpolation ) 17
3-5 小節結論 21
第四章 分數延遲濾波器的介紹 22
4-1 理想延遲濾波器 ( Ideal Fractional Delay Filter ) 22
4-2 分數延遲濾波器 ( Fractional Delay Filter ) 24
4-3 分數延遲濾波器近似的設計方法 25
4-3-1積分式的加權最小平方近似 25
4-3-2 切點式的加權最小平方近似 33
4-3-3 小節結論 34
第五章 速率轉換濾波器的設計方法 35
5-1 : 使用現存方法去設計 37
5-2 : 使用低通濾波器設計近似設計 38
5-3 : 使用全通濾波器近似設計 44
5-4 費洛架構 ( Farrow Structure ) 47
第六章 模擬結果 52
6-1 取樣速率未改變 的模擬 52
6-2 取樣速率變快 的模擬 57
6-3取樣速率變慢 的模擬 65
第七章 結論與未來方向 76
參考文獻 77

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