## Kaiser 窗

Kaiser 窗近似于扁长椭圆形窗，它使主瓣能量与旁瓣能量之比最大。对于特定长度的 Kaiser 窗，参数 β 控制相对旁瓣衰减。对于给定的 β，相对旁瓣衰减相对于窗长度是固定的。语句 kaiser (n,beta) 计算长度为 n、参数为 beta 的 Kaiser 窗。

n = 50; w1 = kaiser(n,1); w2 = kaiser(n,4); w3 = kaiser(n,9); [W1,f] = freqz(w1/sum(w1),1,512,2); [W2,f] = freqz(w2/sum(w2),1,512,2); [W3,f] = freqz(w3/sum(w3),1,512,2); plot(f,20*log10(abs([W1 W2 W3]))) grid legend('\beta = 1','\beta = 4','\beta = 9')

w1 = kaiser(50,4); w2 = kaiser(20,4); w3 = kaiser(101,4); [W1,f] = freqz(w1/sum(w1),1,512,2); [W2,f] = freqz(w2/sum(w2),1,512,2); [W3,f] = freqz(w3/sum(w3),1,512,2); plot(f,20*log10(abs([W1 W2 W3]))) grid legend('length = 50','length = 20','length = 101') 

### 在 FIR 设计中使用 Kaiser 窗

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

$n=\frac{\alpha -8}{2.285\Delta \omega }+1$

[n,wn,beta] = kaiserord([0.4 0.6]*pi,[1 0],[0.01 0.01],2*pi); h = fir1(n,wn,kaiser(n+1,beta),'noscale');

kaiserord 函数估计滤波器阶数、截止频率和 Kaiser 窗 beta 参数，使之满足一组给定的频域设定。

fvtool(h,1)