在本篇論文中, 我們的基礎理論是凸集最佳化(Convex Optimization) 理論[1] 。
而我們研究的議題是如何將濾波器設計問題, 轉換為凸集最佳化問題。如此可確保找到
的解, 為全域(Globally) 最佳解。當我們得到濾波器係數後, 將其量化, 藉由文獻[2]建
議的演算法, 降低其所需量化位元數。最後, 我們嘗試改變量化的順序, 並與文獻[2]方
法的結果做比較。

In this thesis, the basic theory is convex optimization theory[1]. And we study
the problem about how to transfer to convex optimization problem from the filter
design problem. So that we can guarantee the solution is the globally optimized
solution. As we get the filter coefficients, we quantize them, then to reduce the
quantization bits of the filter coefficients by using the algorithm[2]. At last, we try
to change the sequence of quantization, and compared the result with the result of
the method[2].

摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .i
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ii
目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .iii
圖次. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
表次. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .vii
1 緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
2 研究問題描述. . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1 有限脈衝響應濾波器(Finite-Duration Impulse Response filter, FIR) . . . . . . . . . . . . . . . . . . . . . . . . . .2
2.2 無限脈衝響應濾波器(Infinite-Duration Impulse Response filter, IIR) . . . . . . . . . . . . . . . . . . . . . . . . . . .3
2.3 量化濾波器係數. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3 使用凸集最佳化理論設計有限脈衝響應濾波器. . . . . .5
3.1 線性相位(Linear Phase) 濾波器. . . . . . . . . . . . . . . . 5
3.1.1 運用脈衝響應對稱特性. . . . . . . . . . . . . . . . . . . . . . .6
3.1.2 使用Quadratic Program 設計線性相位濾波器. . . 9
3.2 非線性相位濾波器. . . . . . . . . . . . . . . . . . . . . . . . . . . .14
3.2.1 Linear Program . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
3.2.2 Semidefinite Program . . . . . . . . . . . . . . . . . . . . . .17
3.2.3 Minimax(Chebyshev) 設計. . . . . . . . . . . . . . . . . . .20
4 使用凸集最佳化理論設計無限脈衝響應濾波器. . . . . .26
5 降低量化位元數 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
6 結論 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
7 附錄 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
7.1 軟體使用說明. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45
7.1.1 軟體適用環境. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45
7.1.2 CVX安裝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
7.1.3 FIR使用方法與範例說明. . . . . . . . . . . . . . . . . . . . .47
7.1.4 量化. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49
7.1.5 IIR使用方法與範例說明. . . . . . . . . . . . . . . . . . . . . 50
參考文獻 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

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