北理工数字信号处理实验3 IIR数字滤波器设计

实验3IIR数字滤波器设计一、实验目的1、掌握利用脉冲响应不变法和双线性变换法设计IIR数字滤波器的原理及具体方法2、加深理解数字滤波器和模拟滤波器之间的技术指标转化3、掌握脉冲响应不变法和双线性变换法设计IIR数字滤波器的优缺点及适用范围二、实验设备与环境计算机、MATLAB软件环境三、实验理论基础四、实验内容解：（1）巴特沃斯Wn=0.2*pi;Rp=1;As=15;N=6;[b,a]=butter(N,Wn,'s');[bz,az]=impinvar(b,a);[H,w]=freqz(bz,az);subplot(221);plot(w/pi,abs(H));gridon;xlabel('\Omega(\pi)');ylabel('|H(j\Omega)|');subplot(222);plot(w/pi,20*log10((abs(H))/max(abs(H))));gridon;xlabel('Omega(\pi)');ylabel('|H(j\Omega)|,dB');subplot(223);plot(w/pi,angle(H)/pi);gridon;xlabel('Omega(\pi)');ylabel('PhaseofH(j\Omega)(\pi)');t=0:0.01:30;h=impulse(b,a,t);subplot(224);plot(t,h);gridon;xlabel('t(s)');ylabel('ImpulseResponse');00.5100.51()|H(j)|00.51-100-500Omega()|H(j)|,dB00.51-1-0.500.51Omega()PhaseofH(j)()0102030-0.100.10.20.3t(s)ImpulseResponse（2）切比雪夫1Wn=0.2*pi;Rp=1;N=6;[b,a]=cheby1(N,Rp,Wn,'s');[bz,az]=impinvar(b,a);[H,w]=freqz(bz,az);subplot(221);plot(w/pi,abs(H));gridon;xlabel('\Omega(\pi)');ylabel('|H(j\Omega)|');subplot(222);plot(w/pi,20*log10((abs(H))/max(abs(H))));gridon;xlabel('Omega(\pi)');ylabel('|H(j\Omega)|,dB');subplot(223);plot(w/pi,angle(H)/pi);gridon;xlabel('Omega(\pi)');ylabel('PhaseofH(j\Omega)(\pi)');t=0:0.01:30;h=impulse(b,a,t);subplot(224);plot(t,h);gridon;xlabel('t(s)');ylabel('ImpulseResponse');00.5100.51()|H(j)|00.51-150-100-500Omega()|H(j)|,dB00.51-1-0.500.51Omega()PhaseofH(j)()0102030-0.100.10.20.3t(s)ImpulseResponse（3）切比雪夫2Wn=0.3*pi;As=15;N=6;[b,a]=cheby2(N,As,Wn,'s');[bz,az]=impinvar(b,a);[H,w]=freqz(bz,az);subplot(221);plot(w/pi,abs(H));gridon;xlabel('\Omega(\pi)');ylabel('|H(j\Omega)|');subplot(222);plot(w/pi,20*log10((abs(H))/max(abs(H))));gridon;xlabel('Omega(\pi)');ylabel('|H(j\Omega)|,dB');subplot(223);plot(w/pi,angle(H)/pi);gridon;xlabel('Omega(\pi)');ylabel('PhaseofH(j\Omega)(\pi)');t=0:0.01:30;h=impulse(b,a,t);subplot(224);plot(t,h);gridon;xlabel('t(s)');ylabel('ImpulseResponse');00.5100.511.52()|H(j)|00.51-15-10-50Omega()|H(j)|,dB00.51-1-0.500.51Omega()PhaseofH(j)()0102030-1-0.500.5t(s)ImpulseResponse（4）椭圆Wn=0.2*pi;Rp=1;As=15;N=6;[b,a]=ellip(N,Rp,As,Wn,'s');[bz,az]=impinvar(b,a);[H,w]=freqz(bz,az);subplot(221);plot(w/pi,abs(H));gridon;xlabel('\Omega(\pi)');ylabel('|H(j\Omega)|');subplot(222);plot(w/pi,20*log10((abs(H))/max(abs(H))));gridon;xlabel('Omega(\pi)');ylabel('|H(j\Omega)|,dB');subplot(223);plot(w/pi,angle(H)/pi);gridon;xlabel('Omega(\pi)');ylabel('PhaseofH(j\Omega)(\pi)');t=0:0.01:30;h=impulse(b,a,t);subplot(224);plot(t,h);gridon;xlabel('t(s)');ylabel('ImpulseResponse');00.5100.511.5()|H(j)|00.51-40-30-20-100Omega()|H(j)|,dB00.51-1-0.500.51Omega()PhaseofH(j)()0102030-0.100.10.20.3t(s)ImpulseResponse五、实验心得与体会通过本次实验，掌握了利用脉冲响应不变法和双线性变换法设计IIR数字滤波器的原理及具体方法；加深理解了数字滤波器和模拟滤波器之间的技术指标转化；掌握了脉冲响应不变法和双线性变换法设计IIR数字滤波器的优缺点及适用范围，MATLAB操作更加熟练。