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

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.

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

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Sept. 1999.
[5] http://www.math.tku.edu.tw/chinese/mathhall/request/4order.pdf