本篇論文提出一個分析與合成正交鏡像濾波器組(QMF)的快速演算法和硬體設計，在數位廣波(DRM)中的頻帶複製法(SBR)裡會大量使用到此濾波器組，前後處理與核心快速傅立葉轉換(FFT)運算，以這兩種快速演算法實現正交鏡像濾波器組。在FFT核心，本論文使用Radix-2架構，可以使分析正交鏡像濾波器組(AQMF)減少最後一級蝴蝶運算的加法量，並可以計算出合成正交鏡像濾波器組(SQMF)。此外，本論文使用Lifting Scheme乘法技巧，以降低複數乘法所造成的實數乘法與加法量。在32通道的AQMF與原始定義運算量相比，乘法量降低87.99%，加法量降低73.51%，係數減少95.31%。在32通道的SQMF與Hsu et al.[13]文獻相比，乘法量降低51.54%，加法量降低21.12%，係數減少78.57%。因此，在未來的DRM應用中，本論文提出的快速演算法與其它文獻的方法相比，有更低的運算量與更高的相容性。

This brief presents a novel fast algorithm derivation and structure design of analysis and synthesis quadrature mirror filterbanks (SQMF) on the spectral band replication (SBR) in Digital Radio Mondiale (DRM). After pre- and post-procedures, a Fourier transform-based (FT-based) computational kernel was required to construct two types of fast algorithms that offered certain advantages. The proposed method employs a modified radix-2 fast Fourier transform (FFT) for analysis QMF (AQMF) to reduce the number of additions at the last stage of the butterfly, and adopts a radix-2 FFT to calculate the SQMF coefficients. In addition, a well-known lifting scheme (LS) was applied to reduce numerous multiplication and addition calculations. Compared with the original calculations for the long transform length, all multiplication, addition, and coefficient operations for the Proposed method AQMF had 87.99%, 73.51%, and 95.31% reductions, respectively. Compared with the fast SQMF algorithm by Huang et al., the Proposed method for SQMF reduces 51.54% of the multiplication, 21.12% of the addition, and 78.57% of the coefficients. Therefore, the proposed fast QMF algorithm is a better solution than other approaches for future DRM applications.

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