数字滤波器设计(2)

A =

1.0e+255 *

Columns 1 through 18

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Columns 19 through 36

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Columns 37 through 54

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Columns 55 through 59

0.0000 0.0000 0.0000 0.0069 4.7947

B =

1.0e+255 *

Columns 1 through 18

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Columns 19 through 36

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Columns 37 through 54

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Columns 55 through 59

0 0 0 0 4.7947

0.0000 0.0000 0.0000 0.0000 0 0 0 0 0 0 3.2. 双线性变换法 3.2.1. 程序 Fs=20000; wpz=8000/Fs wsz=9000/Fs; Rp=0.5; As=50;

wp=2*tan(wpz*pi /2); ws=2*tan(wsz*pi/2);

[N,wc]=buttord(wp,ws,Rp,As,'s'); [B,A]=butter(N,wc,'s'); [Bz,Az]=bilinear(B,A,Fs);

[Nd,wdc]=buttord(wpz,wsz,Rp,As); [Bdz,Adz]=butter(Nd,wdc); k=0:511;

fk=0:20000/512:20000;

wk=2*pi*fk;Hk=freqs(B,A,wk);plot(fk/1000,20*log10(abs(Hk))); grid on;

xlabel('频率/kHz'); ylabel('幅值/dB'); axis([0,2,-4000,0]);

3.2.2. 幅频响应损耗函数曲线

A =

1.0e+014 *

Columns 1 through 18

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0004 0.0011 0.0030 0.0075 0.0174 0.0373

Columns 19 through 36

0.0742 0.1372 0.2361 0.3785 1.2334 1.3849 1.4437 1.3943 0.5320 0.3329 0.1877 0.0946

Columns 37 through 44

0.0421 0.0163 0.0054 0.0015 0.0000 B =

1.0e+007 *

Columns 1 through 18

0 0 0 0 0 0 0 0 0 0 0 0

Columns 19 through 36

0 0 0 0 0 0 0 0 0 0 0 0

Columns 37 through 44

0 0 0 0 3.1532

0.5655 1.2445 0.0003 0 0 0 0 0 0.7875 1.0233 0.0001 0 0 0 0 0 1.0215 0.7721 0.0000 0 0 0 0 0 4. 采用窗函数法（分别用汉宁窗、哈明窗、布莱克曼窗函数）设计满足要求的

FIR低通滤波器，求出h(n)，并画出幅频响应损耗函数曲线. 4.1. 汉宁窗 4.1.1. 程序 Fs=20000; fp=4000; fs=4500; m=[1 1 0 0]; wp=2*pi*fp/Fs; ws=2*pi*fs/Fs; Rp=0.5; As=50; Bt=ws-wp;

N0 = ceil (6.6* pi /Bt); N=N0+mod(N0+1,2); wc=(wp+ws)/2/pi;

hn=fir1(N-1,wc,hanning(N)); freqz(hn,1,512);

plot (w,20*log(abs(hn))); grid;

axis ([0 ,1, -1000 , 100]); xlabel('频率/kHz'); ylabel('幅值/dB');

4.1.2. 滤波器h(n)的波形及其幅频响应损

4.2. 哈明窗 4.2.1. 程序

Fs=20000; fp=4000; fs=4500; m=[1 1 0 0]; wp=2*pi*fp/Fs; ws=2*pi*fs/Fs; Rp=0.5; Rs=50; Bt=ws-wp;

N0 = ceil (6.6* pi /Bt); N=N0+mod(N0+1,2); wc=(wp+ws)/2/pi;

hn=fir1(N-1,wc,hamming(N)); freqz(hn,1,512);

plot (w,20*log(abs(hn))); grid on;

axis ([0 ,1, -1000 , 100]); xlabel ('频率/kHz'); ylabel ('幅值/dB' );

4.2.2. 滤波器h(n)的波形及其幅频响应损耗函数曲线