本篇論文提出一個以遞迴式離散餘弦第四型轉換(DCT-IV)為核心來實現修正型正、逆離散餘弦轉換(MDCT / IMDCT )的快速演算法，並應用於各種音訊壓縮技術中的分析與合成濾波器組(Analysis and Synthesis Filter Banks)。該處理器可支援MP3、AAC、AAC in DRM、AAC in DAB、AC-3、TwinVQ、Ogg等多格式之共架構，除此之外，針對HE-AAC音訊規格，還能支援高品質頻帶複製技術(HQ-SBR)與低功率頻帶複製技術(LP-SBR)中分析正交鏡像濾波器組(AQMF)與合成正交鏡像濾波器組(SQMF)的運算。
此架構透過前、後處理將MDCT/IMDCT/AQMF/SQMF運算轉化成共用的DCT-IV型式，再將一維DCT-IV分別拆解成DCT-III與DCT-II運算的二維型式演算法，藉此來提升遞迴架構的硬體效能，與近期Li et al.所發展的新式演算法相比，其整體運算週期為我們的7.5倍，而乘法運算量為我們的4.2倍，加法運算量為我們的3.1倍，係數需求量為我們的54.1倍。
在硬體實現上，所提之電路架構僅需8個乘法器與10個加法器，我們以Altera-based platform來實現所設計之架構，其操作頻率最高為41MHz，適合應用於支援多格式的音訊編解碼器。

This thesis proposes a fast MDCT / IMDCT algorithm whose kernel is adopted the recursive DCT-IV. It applies for analysis and synthesis filterbanks in audio codecs. This proposed design is supporting multi-standards, such as MP3、AAC、AAC in DRM、AAC in DAB、AC-3、TwinVQ、Ogg etc. Furthermore, this architecture can compute AQMF/SQMF in HQ-SBR and LP-SBR for HE-AAC.
To implement the unified architecture design of analysis and synthesis filterbanks, MDCT/IMDCT/AQMF/SQMF are converted to DCT-IV by pre-processing and post- processing. Moreover, in order to improve performance of recursive DCT-IV, we decompose the one-dimensional DCT-IV to two-dimensional algorithm by DCT-III and DCT-II. Compare with the latest algorithm proposed by Li et al, whose computing cycle is 7.5 times than proposed algorithm, Multiplication is 4.2 times, addition is 3.1 times and coefficient requirment is 54.1 times.
This proposed design only costs 8 Multiplier and 10 Adder for implementation. It is implemented by using Altera-based platform, and max clock rate is 41MHz. The design is suitable for multi-standard audio codecs.

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