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論文名稱 Title |
用Tschirnhaus轉換的方式計算線頻譜對 The Computation of Line Spectrum Pair Frequencies Using Tschirnhaus Transform |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
46 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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口試日期 Date of Exam |
2009-01-20 |
繳交日期 Date of Submission |
2009-02-02 |
關鍵字 Keywords |
Tschirnhaus 轉換、線頻譜對、四次方程 quartic equation, Tschirnhaus Transform, LSP |
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統計 Statistics |
本論文已被瀏覽 5760 次,被下載 2992 次 The thesis/dissertation has been browsed 5760 times, has been downloaded 2992 times. |
中文摘要 |
Tschirnhaus轉換是一種解四次多項式方程的方式.如果四次方程的4個根都是相異實數,我們可以導出一個簡單的公式來降低10階線頻譜對的計算複雜度.但在計算過程中取反三角函數會增加在應用硬體上的計算量,我們將討論一些方法取代它,使得晶片計算更加迅捷.同時附上和改良型無複數 Farrari公式計算結果的比較表 |
Abstract |
The Tschirnhaus Transform is a method to solve quartic equations. If the quartic equation has four distinct real roots, a low computation complexity algorithm is proposed and applied to the the 10-order Line Spectrum Pairs(LSP).However, during the procedures of calculation, the existence of the inverse trigonometric functions increase the computation load of the hardware implementation. We also propose some methods to solve this problem and increase the speed of the calculation. A table of comparison result with the previous proposed Complex-Free Farrari formula is also included. |
目次 Table of Contents |
1 Introduction 5 2 Line Spectrum Pair Frequencies 7 3 Tschirnhaus Transform 9 4 Approximate cosθ/3 by some methods 21 5 Compared with the Modified Complex-Free Farrari Formula 35 6 Solve 10-order LSP 39 Reference 41 |
參考文獻 References |
[1] S. H. Chen, Yaotsu Chang, and J. C. Ruan, ”An Efficient Computation of LSP Frequencies Using Modified Complex-Free Ferrari Formula,” Journal of Signal Processing Systems, Vol. 52, No. 2, pp.153-163, Aug. 2008. [2] F. K. Soong and B. H. Juang, ”Line spectrum pair (LSP) and speech data compression,” in Proc. ICASSP-84, pp. 1.10.1-1.10.4, Mar.1984. [3] P. Kabal and R. P. Ramachandran, ”Computation of line spectral frequencies using Chebyshev polynomials,” IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP-34, pp. 1419-1426, Dec 1986. [4] J. Rothweiler, ”On polynomial reduction in the computation of LSP frequencies,” IEEE Trans. Speech Audio Processing, vol. 7, pp. 592-594, Sept. 1999. [5] http://www.math.tku.edu.tw/chinese/mathhall/request/4order.pdf |
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