本篇論文提出兩個遞迴式架構為基礎的分析與合成正交鏡像濾波器(QMF)的快速演算法，在數位廣波(DRM)中的各種音訊編碼會使用到此種濾波器。在所提出的第一種快速演算法中，透過輸入訊號的重新排列可以將遞迴核心的係數合併以及常數化，再搭配CSD乘法器技術可使得此核心的乘法運算量以及係數使用量大幅降低。在所提出的第二種快速演算法中，透過輸入訊號的折疊使得訊號在遞迴核心內遞迴次數降低，進而有效降低乘法運算量以及加法運算量。遞迴式的核心架構使得此二種快速演算法有較大的應用彈性，本論文以其為核心應用在等頻寬濾波器組上，使分頻數可以為奇數以及偶數，比起以FFT為核心的平行架構有著更好的應用範圍。因此，在未來的DRM以及分頻濾波器應用中，本論文可提供更多的選擇性。

This thesis proposed a novel fast algorithm and common structure design of analysis and synthesis quadrature mirror filterbanks (AQMF, SQMF) on the spectral band replication in digital radio mondiale (DRM). Based on recent Lai et al.’s concept, an extended issue is addressed form the view point of recursively computing the AQMF and SQMF coefficients. The proposed-I method also combines with the lifting scheme algorithm. The results show that the proposed AQMF algorithm has a great improvement on computational complexity. For the recursive kernel computation (N=64), the proposed method has, respectively, 46.38% of multiplication reductions and 20.46% of addition reductions which can cover the shortcoming of the proposed SQMF. It would be more efficient and more suitable than previous works for DRM applications. The proposed-II recursively computational method not only combines with the lifting scheme algorithm but also employs the fixed-coefficient concept to introduce the technique of canonical signed digit (CSD) multiplication. The results show that the proposed QMFs algorithm has a great improvement on multiplication of computational complexity. For the recursive kernel computation (N=64), the proposed method can transfers the constant multiplication into addition by using CSD technique which brings a great improvement in the complexity of multiplication and the requirement of coefficient. It would be more efficient and more suitable than previous works for DRM applications.

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