数据压缩（十一）——QMF滤波器代码验证（matlab）

N=41;

w=0.43;

[h0,h1,g0,g1]=firpr2chfb(N,w);

[H1z,w]=freqz(h0,1,512);

H1_abs=abs(H1z);H1_db=20*log10(H1_abs);

[H2z,w]=freqz(h1,1,512);

H2_abs=abs(H2z);H2_db=20*log10(H2_abs);

%%%%%%%%%%滤波器h0和h1的幅度响应%%%%%%%%%%

figure(1); 

plot(w/pi,H1_db,'-',w/pi,H2_db,'--');


axis([0,1,-100,10]); 

grid 

xlabel('\omega/\pi');ylabel('幅度,dB'); 

sum1=H1_abs.*H1_abs+H2_abs.*H2_abs;


d=10*log10(sum1);

%%%%%%%%%%%%幅度响应关系误差%%%%%%%%%%%%%

figure(2) 

plot(w/pi,d);grid; 

xlabel('\omega/\pi');ylabel('误差,dB'); 

axis([0,1,-0.04,0.04]); 

%%%%%%%%%%%%%x1(n)%%%%%%%%%%%%%%%%%%%%%

x=zeros(1,500);

x(2)=1;x(3)=1;

x(6)=2;x(7)=2;x(8)=2;

x(17)=1.5;x(18)=1.5;x(19)=1.5;

x(24)=1;x(25)=1;

x(33)=3;x(34)=3;x(35)=3;

%%%%%%%%%%%%%%x2(n)%%%%%%%%%%%%%%%%%%%%

x=zeros(1,500);

x(1)=1;x(2)=1;x(3)=1;

x(9)=2;x(10)=2;x(11)=2;

x(16)=3;x(17)=3;x(18)=3;

x(24)=4;x(25)=4;x(26)=4;

x(33)=3;x(34)=3;x(35)=3;

x(41)=2;x(42)=2;x(43)=2;

x(49)=1;x(50)=1;x(51)=1;

%%%%%%%%%%%%%%x3(n)%%%%%%%%%%%%%%%%%%%%

n=1:500;

T=0.2;

x=sin(n*T);

hlp=mfilt.firdecim(2,h0);

hhp=mfilt.firdecim(2,h1);

glp=mfilt.firinterp(2,g0);

ghp=mfilt.firinterp(2,g1);

x0=filter(hlp,x);

x0=filter(glp,x0);

x1=filter(hhp,x);

x1=filter(ghp,x1);

xidle=x0+x1;

xshift=[zeros(1,N) x(1:end-N)];

e=xidle-xshift;

mes=sum(abs(e).^2)/length(e)

fvtool(h0)

%%%%%%%%%%%%输入信号%%%%%%%%%%%%%%%%%%

figure(4);

plot(x);

%%%%%%%%%%理想输出信号与重建输出信号%%%%%%%

figure(5);

axis([0,500,-1,1]); 

plot(xshift,'r');hold on;

plot(xidle,'-');

axis([0,600,-1.1,1.1]);

%%%%%%%理想输出信号与重建输出信号的偏差%%%%%%

figure(6);

plot(xshift-xidle);

输出结果

h1和h0的幅度响应镜像对称，衰减的部分可以相互抵消，滤波器把原本的频带分解为两个子带。

幅度相应关系差大部分均为10，即使波动也不超过0.02.，所哟所以误差很小。

h0的幅度响应，从波形直观上来看，极接近理想波形。通带为一条直线，过渡带很窄，下降很快，阻带最大值为70dB。

输入信号。
理想输出信号与重建输出信号
理想输出信号与重建输出信号的偏差，偏差较小，10^-4.