QMF滤波器分析zhaly615的博客-

【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')