臺灣博碩士論文加值系統

離散正弦轉換(DST)可應用於不同的領域，包含資料壓縮、數位濾波、影像重建、影像編碼等。
本文介紹的DST遞迴演算法，具有下列的結構，可從兩個完全相同低點數的DST來產生一個高點數的DST，以遞迴的DST這個方法作為工具，可得到的結果是比其他演算法，更為減少的乘法器和加法器數量。

The discrete sine transform(DST) is widely applied in various fields , including image data compression and digital filtering, image reconstraction, and image coding . This paper presents a recursive algorithm for DST with a structure that allows the generation of the next higher order DST from two identical lower order DST’s. As a result, the method for implementing this recursive DST requires fewer multipliers and adders than other DST algorithms.

中文摘要 i
英文摘要 ii
致謝 iii
目錄 iv
圖目錄 v
表目錄 vi
第一章 緒論 1
1.1 研究動機 1
1.2 研究目的 2
1.3 研究方法 3
1.4 回顧相關文獻研究 4
1.5 論文大綱 5
第二章 相關演算法原理分析 6
2.1 離散傅立葉轉換(DFT) 6
2.2 分時FFT演算法(Decmiation-in-time FFT algorithms) 7
2.3 分頻FFT演算法(Decimation-in-frequency FFT algorithms) 14
2.4 哥茲柔演算法(The Goertzel algorithm) 19
2.5 庫利—塔基演算法(Cooley-Tukey Algorithms) 21
2.6 質因數演算法 29
2.7 維諾格雷得傅氏轉換演算法的概述(Overview of
the Winograd Fourier Transform Algorithm) 33
第三章 離散正弦轉換的分類及性質 34
3.1 第一類DST-I 34
3.2 第二類DST-II 35
3.3 第三類DST-III 35
3.4 第四類DST-IV 36
第四章 DST實例與固有特性 37
4.1 DST定義和三個實例 37
4.1.1 DST三個實例的推算過程 39
4.2 DST的固有特性 47
第五章 快速遞迴演算法與特徵系統 50
5.1 快速遞迴演算法 50
5.2 特徵系統 53
第六章 數位訊號在實踐時的說明 56
第七章 結論與未來展望 60
參考文獻 61
附錄 發表於“2006年全國電信研討會”之論文 65

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