扰动次数

扰动形式

扰动参数取值

生成函数

一次

${\alpha }_1\left(z^{-1}+z-2\right)+1$

${\alpha }_1=-\frac{j}{8}$

$S=\frac{2z^{-\frac{j}{2}}{\left(1+z\right)}^j\left(-\frac{j}{8}{z}^{-1}+\left(1+\frac{j}{4}\right)-\frac{j}{8}z\right)}{2^j}$

二次

${\displaystyle \sum }_{k=1}^2{\alpha }_k\left(z^{-k}+z^k-2\right)+1$

${\alpha }_1=-4{\alpha }_2-\frac{j}{8}$

$S=\frac{\begin{array}{l}2z^{-\frac{j}{2}}{\left(1+z\right)}^j({\alpha }_2{z}^{-2}+\left(-4{\alpha }_2-\frac{j}{8}\right)z^{-1}\\ +\left(1+6{\alpha }_2+\frac{j}{4}\right)+\left(-4{\alpha }_2-\frac{j}{8}\right)z+{\alpha }_2{z}^2)\end{array}}{2^j}$ ， ${\alpha }_2$ 为任意值

三次

${\displaystyle \sum }_{k=1}^3{\alpha }_k\left(z^{-k}+z^k-2\right)+1$

${\alpha }_1=-4{\alpha }_2-9{\alpha }_3-\frac{j}{8}$

$S=\frac{\begin{array}{l}2z^{-\frac{j}{2}}{\left(1+z\right)}^j({\alpha }_3{z}^{-3}+{\alpha }_2{z}^{-2}+\left(-4{\alpha }_2-9{\alpha }_3-\frac{j}{8}\right)z^{-1}\\ +\left(1+6{\alpha }_2+16{\alpha }_3+\frac{j}{4}\right)+\left(-4{\alpha }_2-9{\alpha }_3-\frac{j}{8}\right)z+{\alpha }_2{z}^2+{\alpha }_3{z}^3)\end{array}}{2^j}$ ， ${\alpha }_2,{\alpha }_3$ 为任意值