采用窗函数法设计一个数字FIR低通滤波器,其技术指标为：wp=0.2pi,ws=0.3pi,rp0.25db,as=50

结合衰减和过度带,可选择哈明窗.尽管在设计中,没有使用通带波动值Rp,但必须检查设计的实际波动,验证它是否确实在给定容限内.对应的MATLAB程序为：
wp= 0.2* pi; ws = 0.3 *pi;
tr_width = ws –wp; %确定过度带宽
M = ceil (6.6* pi /tr_width) +1 ；% 确定滤波器阶数 ,ceil是向上取整函数
n = [0:1:M-1];
wc = (ws +wp ) /2; %理想低通的截止频率
hd = ideal _lp (wc,M);
w_ham = (hamming (M))’;
h = hd .* w_ham;
[db,mag,pha,grd,w]=freqz_m (h,[1]);
delta _w =2*pi/1000;
Rp= - (min (db(1:1:wp/ delta _w +1))); %实际通带波动
As= - round (max (db (ws/delta_w +1:1:501 ))) ；% 最小阻带衰减
%画图 （见图1-5-1）
subplot (2,2,1); stem(n,hd ); title (‘理想冲激响应’);
axis ([0 ,M-1,-0.1 ,0.3]); xlabel (‘n’); ylabel (‘hd(n)’ );
subplot (2,2,2); stem(n,w_ham ); title (‘哈明窗’);
axis ([0 ,M-1,0 ,1.1]); xlabel (‘n’); ylabel (‘w(n)’ );
subplot (2,2,3); stem(n,h ); title (‘实际冲激响应’);
axis ([0 ,M-1,-0.1 ,0.3]); xlabel (‘n’); ylabel (‘h(n)’ );
subplot (2,2,4); plot (w/pi,db ); title (‘幅度响应（单位：dB）’); grid
axis ([0 ,1,-100 ,10]); xlabel (‘频率（单位：pi）’); ylabel (‘分贝数’ );
根据以上代码,可计算出滤波器阶数M=67,实际的阻带衰减As=52dB,实际的通带波动为Rp=0.0394 dB,满足设计技术指标.