FIR滤波器设计方法.doc

实验5 FIR滤波器设计方法模拟原型Butterworth滤波器： wp=0.4*pi;ws=0.6*pi;Rp=0.5;As=50; b,a=afd_butt(wp,ws,Rp,As);* Butterworth Filter Order = 17 db,mag,pha,w=freqs_m(b,a,pi); ha,x,t=impulse(b,a,100); subplot(2,2,1);plot(w/pi,mag);xlabel(w);ylabel(|H|);grid on subplot(2,2,2);plot(w/pi,pha);xlabel(w);ylabel(相位); grid on subplot(2,2,3);plot(w/pi,db);xlabel(w);ylabel(db); grid on subplot(2,2,4);plot(t,ha);xlabel(t);ylabel(ha(t); axis(0,100,-0.2,0.4);grid on双线性变换法求得的数字Butterworth低通滤波器： wp=0.4*pi;ws=0.6*pi;Rp=0.5;As=50; T=2;OmegaP=(2/T)*tan(wp/2);OmegaS=(2/T)*tan(ws/2); N=ceil(log10(10(Rp/10)-1)/(10(As/10)-1)/(2*log10(OmegaP/OmegaS); OmegaC=OmegaP/(10(Rp/10)-1)(1/(2*N);wn=2/pi*atan(OmegaC*T/2); b,a=butter(N,wn); db,mag,pha,grd,w = freqz_m(b,a); n=0:100; h=impz(b,a,n); subplot(2,2,1);plot(w/pi,mag);xlabel(w);ylabel(|H|); axis(0,1,0,1.15);grid on subplot(2,2,2);plot(w/pi,pha);xlabel(w);ylabel(相位); axis(0,1,-4,4); grid on subplot(2,2,3);plot(w/pi,db);xlabel(w);ylabel(db); axis(0,1,-140,20); grid on subplot(2,2,4);stem(n,h);xlabel(n);ylabel(h(n); axis(0,100,-0.2,0.4);grid on由前面的数字Butterworth低通滤波器映射得到的高通滤波器：接上面的程序 wp1=ws;ws1=wp; N1,wn1=buttord(wp1/pi,ws1/pi,Rp,As); b1,a1=butter(N1,wn1,high); db1,mag1,pha1,grd1,w1 = freqz_m(b1,a1); h1=impz(b1,a1,n);subplot(2,2,1);plot(w1/pi,mag1);xlabel(w1);ylabel(|H1|);axis(0,1,0,1.15);grid onsubplot(2,2,2);plot(w1/pi,pha1);xlabel(w1);ylabel(相位); axis(0,1,-4,4); grid onsubplot(2,2,3);plot(w1/pi,db1);xlabel(w1);ylabel(db1); axis(0,1,-140,20); grid on subplot(2,2,4);stem(n,h1);xlabel(n);ylabel(h1(n); grid on信号x(n)通过数字Butterworth低通滤波器：接上面程序 w1=0.3*pi;w2=0.7*pi; x=cos(w1*n)+cos(w2*n); y,ny=conv_m(x,n,h,n); X=dtft(x,n,w); Y=dtft(y,ny,w); magX=abs(X);magY=abs(Y);figure(2); subplot(2,2,1);stem(n,x);xlabel(n);ylabel(x(n);grid on subplot(2,2,2);plot(w/pi,magX);xlabel(w);ylabel(幅度|X|); grid on subplot(2,2,3);stem(ny,y