本論文提出兩個基於固定係數第二型離散正弦轉換架構，支援正、逆改進型離散正餘弦轉換。改進型離散餘弦轉換被使用在許多音訊編解碼器中，包括：進階音訊編碼(AAC(MPEG-4))、AC-3、ATRAC1、ATRAC3plus、CELT、MP3 (MPEG-1, 2, 2.5 Audio Layer III)、Opus (Hybrid mode)、Real Audio、Vorbis (Ogg)、Windows Media Audio Standard、和Windows Media Audio Pro等等。最近MPEG (Motion Pictures Experts Group)發表的3D編解碼器同時被稱作Unified Speech and Audio Coding (USAC)，改進型離散正餘弦轉換皆被使用在其中一種complex stereo prediction。
由於改進型離散正餘弦轉換皆可以用第四型離散正弦轉換表示，而且第四型離散正弦轉換又可以被推導成四種第二型離散正弦轉換型式，因此改進型離散正餘弦轉換可以以第二型離散正弦轉換型式呈現。這裡提出的第一個第二型遞迴離散正弦轉換架構僅需一個乘法器、三個加法器和兩個延遲來實現，且乘法器還能用CSD (Canonical Signed Digit)乘法器的方式以更少的位移器和加法器取代掉全部的乘法運算量。這裡品質因子(Q factor)被用來確保系統在最穩定的狀態。為了加速設計，因此又提出一個輸入摺疊過的第二型離散正弦轉換架構，這個架構的運算週期數為第一個的一半，運算複雜度與引用的過去文獻比較下能達到大約四分之一的運算量。
為了使用硬體描述語言來驗證提出的第二型離散正弦轉換架構，這裡先以MATLAB確認架構中的節點和係數所需位元數，然後再在Altera 的 DSP Builder中將架構建好和調整成確認後的位元長度。跑過Signal Compiler和Testbench工具後，所提出的第二型離散正弦轉換架構即可在Quartus II 和Modelsim中被program和驗證。而所跑出的峰值信噪比(PSNR)皆超過90dB，符合音訊的規格。

This thesis proposes a signed DST-II fixed coefficient kernel for implementing MDST and MDCT designs. MDCT is used in various audio codecs including Advanced Audio Codec (AAC (MPEG-4)), AC3, ATRAC1, ATRAC3, ATRAC3plus, CELT, MP3 (MPEG-1, 2, 2.5 Audio Layer III), Opus (Hybrid mode), Real Audio, Vorbis (Ogg), Windows Media Audio Standard, and Windows Media Audio Pro. In the recently developed 3D audio codec also known as Unified Speech and Audio Coding (USAC) by MPEG, both MDCT and MDST are used in one of the two forms of complex stereo prediction.
Since MDCT and MDST can both be represented as a DST-IV transform, and DST-IV transform can be further derived into 4 transforms represented by DST-II, MDCT and MDST can both be realized by DST-II kernel. The Proposed DST-II structure requires only one multiplier, three adders and two delays in implementation. Additionally, the multiplier can be further replaced by fewer shifters and adders using CSD representation. A q factor is used to minimize quantization effect.
To verify the DST-II kernel running in hardware description language, the node and coefficient bits required for the kernel are configured by MATLAB, and the structure of the kernel with configured word length is built in Altera’s DSP Builder. By running the Signal Compiler and Testbench tool, the signed DST-II kernel is programmed and verified in Quartus II and Modelsim. And the PSNR of extracted output values exceeds 90dB, which is suitable for audio implementation.

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