# kaiser

Kaiser 窗

## 语法

``w = kaiser(L,beta)``

## 说明

``w = kaiser(L,beta)` 返回形状因子为 `beta` 且长度为 `L` 个点的 Kaiser 窗。`

## 示例

```w = kaiser(200,2.5); wvtool(w)```

## 输出参数

Kaiser 窗，以列向量形式返回。

## 算法

Kaiser 窗的系数由以下方程计算：

`$w\left(n\right)=\frac{{I}_{0}\left(\beta \sqrt{1-{\left(\frac{n-N/2}{N/2}\right)}^{2}}\right)}{{I}_{0}\left(\beta \right)},\text{ }0\le n\le N,$`

`besseli(0,beta*sqrt(1-(((0:L-1)-(L-1)/2)/((L-1)/2)).^2))/besseli(0,beta)`

`$\beta =\left\{\begin{array}{ll}0.1102\left(\alpha -8.7\right),\hfill & \alpha >50\hfill \\ 0.5842{\left(\alpha -21\right)}^{0.4}+0.07886\left(\alpha -21\right),\hfill & 50\ge \alpha \ge 21\hfill \\ 0,\hfill & \alpha <21\hfill \end{array}$`

## 参考

[1] Digital Signal Processing Committee of the IEEE Acoustics, Speech, and Signal Processing Society, eds. Selected Papers in Digital Signal Processing. Vol. II. New York: IEEE Press, 1976.

[2] Kaiser, James F. "Nonrecursive Digital Filter Design Using the I0-Sinh Window Function." Proceedings of the 1974 IEEE® International Symposium on Circuits and Systems. April, 1974, pp. 20–23.

[3] Oppenheim, Alan V., Ronald W. Schafer, and John R. Buck. Discrete-Time Signal Processing. Upper Saddle River, NJ: Prentice Hall, 1999.