QMF滤波器分析

【任务一：调试代码】

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%%%%%%
%理想输出信号与重建的输出信号的偏差%
figure(6);
plot(xshift-xidle);

输出结果：

【任务二】

要求：确定两个长度为100（或其他）的序列，对这两个序列做傅立叶变换，把输出的频谱进行对比。

（1）信号的分解

N=100;                        
n=[0:1:N-1]                  
xn1= normpdf(n, 15, 1)
Xk1=fft(xn1,N);
subplot(411);
stem(n,xn1);
title('xn1原信号');
subplot(412);
stem(n,abs(Xk1));
title('xn1FFT变换')

xn2= normpdf(n, 85, 1)
Xk2=fft(xn2,N);
subplot(413);
stem(n,xn2);
title('xn2原信号');
subplot(414);
stem(n,abs(Xk2));
title('xn2FFT变换')

这里选用了两个均值不同的正态分布函数。

（2）信号的合成

N=100;                        
n=[0:1:N-1]                  
xn= normpdf(n, 15, 1)+normpdf(n, 85, 1)
Xk=fft(xn,N);
subplot(211);
stem(n,xn);
title('xn原信号');
subplot(212);
stem(n,abs(Xk));
title('xn1FFT变换')