MPEG音訊第三層編碼方法(MP3)在今日已被普遍的被應用在數位音訊壓縮上，MP3使用心理聲學模組計算人類聽覺的遮蔽效應，配合可變區塊長度的MDCT、IMDCT、非均勻量化以及熵編碼等等方法強化了音效失真壓縮的效果，而且將能重建的音訊品質保持在讓人類聽覺無法與原始音訊分別的程度。
本論文提出一種可以應用在MP3解碼器端(decoder)的運算方法，這個方法將IMDCT與窗戶函數的運算化為矩陣予以合併，並以積化和差將其轉化為 點的DCT-IV及DCT-III運算，因此可以使用DCT快速演算法以減少實作時的計算量，並且在需要產生的餘弦值數量上，與先前使用 點的DCT的方法比較後有所減少。

The MPEG audio layer three has been applied in digital audio compression generally. It uses the psychoacoustic model, adaptive block length MDCT and IMDCT, nonuniform quantization and entropy coding to enhance the audio compression and keeps quality of the reconstruction audio undifferentiated with the original audio signal for human auditory.
The purposed algorithm is a combined operation of IMDCT and windowing function for MP3 decoder. This algorithm is suitable for fast DCT-IV and DCT-III algorithms for -point that can reduce the computation amount of the implementation. In addition, the required amount of cosine value for the purposed algorithm is less than studies before that use the fast DCT algorithms for -point.

摘要 I
目錄 III
圖目錄 IV
表目錄 VI
第一章 緒論 1
1.1 MP3簡介 1
1.2研究動機及目的 3
1.3論文架構 4
第二章 原理與文獻回顧 5
2.1 MP3音訊編碼方法 5
2.2相關研究探討 15
第三章 研究方法 22
3.1 IMDCT 22
3.2窗戶函數 24
3.3 IMDCT與窗戶函數的合併運算 29
第四章 方法分析 48
第五章 結論 52
參考文獻 53

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