基于数字信号处理课程设计

1、1 设低通df的3db带宽频率wc=0.2,止带频率ws=0.4,在 w=ws处的止带衰减20lg|h(ejws)|=-15db,试用脉冲响应不变法（冲激不变法）设计一个butterworth低通df。(设采样频率fs=20khz）解：依题， 程序如下： wp=input(normalized passband edge =);ws=input(normalized stopband edge =);rp=input(passband ripple in db =);rs=input(minimum stopband attenuation in db =);n,wn=buttord (wp,

2、ws,rp,rs);b,a=butter(n,w n);h,omega=freqz(b,a,512);plot(omega/pi,20*log10(abs(h);grid;xlabel(omega/pi);ylabel(gain db);title(iir butterworth lowpass filter); 仿真的图像如下： 3、试设计一个模拟低通butterworth滤波器解：经计算可知低通butterworth滤波器的阶数为3 用matlab软件计算的程序如下： omegap=0.2*pi;omegas=0.3*pi;rp=7;as=16;n=ceil(log10(10.(0.1*a

3、bs(rp)-1)./(10.(0.1*abs(as)-1)/(2*log10(omegap/omegas)运行程序后出来的结果如下图：使用matlab软件仿真的程序如下： wp=input(normalized passband edge =);ws=input(normalized stopband edge =);rp=input(passband ripple in db =);rs=input(minimum stopband attenuation in db =);n,wn=buttord (wp,ws,rp,rs);b,a=butter(n,wn);h,omega=freqz(

4、b,a,512);plot(omega/pi,20*log10(abs(h);grid;xlabel(omega/pi);ylabel(gain db);title(iir butterworth lowpass filter);得出的仿真波形如下： 4 试用双线性变换法设计butterworth低通df。已知低通df的3db带宽频率，止带起始频率，在 处的止带衰减解：使用matlab软件仿真仿真的程序如下： clc;clear all;omegap=2*pi*2000;omegas=2*pi*4000;rp=3;as=15;g=sqrt(10(as/10)-1)/(10(rp/10)-1);

5、omegar=omegas/omegap;n=ceil(log10(g+sqrt(g*g-1)/log10(omegar+sqrt(omegar*omegar-1);omegac=omegas;z0,p0,k0=cheb2ap(n,as);a0=real(poly(p0);ann=a0(n+1);p=p0*omegac;a=real(poly(p);anu=a(n+1);b0=real(poly(z0);m=length(b0);bnn=b0(m);z=z0*omegac;b=real(poly(z);bnu=b(m);k=k0*(anu*bnn)/(ann*bnu);b=k*bw0=omeg

6、ap,omegas;h,w=freqs(b,a);hx=freqs(b,a,w0);dbhx=-20*log10(abs(hx)/max(abs(h)plot(w/(2*pi)/1000,20*log10(abs(h);xlabel(f(khz);ylabel(db);axis(-1,12,-55,1);set(gca,xtickmode,manual,xtick,0,1,2,3,4,5,6,7,8,9);set(gca,ytickmode,manual,ytick,-50,-40,-30,-20,-10,0);grid;得出的仿真波形如下：1 设chebyshev模拟滤波器的技术指标wc=2

7、p2khz, ws=2p4khz,在w=ws处的衰减小于-15db,通带波动参数，e2 =0.2，求其阶数。解：经计算可知切比雪夫模拟滤波器的阶数为4 用matlab计算的程序如下： clc;clear all;omegap=2*pi*2000;omegas=2*pi*4000;rp=0.17;as=15;g=sqrt(10(as/10)-1)/(10(rp/10)-1);omegar=omegas/omegap;n=ceil(log10(g+sqrt(g*g-1)/log10(omegar+sqrt(omegar*omegar-1)其计算结果显示如下：使用matlab软件仿真程序如下：clc

8、;clear all;omegap=2*pi*2000;omegas=2*pi*4000;rp=0.17;as=15;g=sqrt(10(as/10)-1)/(10(rp/10)-1);omegar=omegas/omegap;n=ceil(log10(g+sqrt(g*g-1)/log10(omegar+sqrt(omegar*omegar-1);omegac=omegas;z0,p0,k0=cheb2ap(n,as);a0=real(poly(p0);ann=a0(n+1);p=p0*omegac;a=real(poly(p);anu=a(n+1);b0=real(poly(z0);m=l

9、ength(b0);bnn=b0(m);z=z0*omegac;b=real(poly(z);bnu=b(m);k=k0*(anu*bnn)/(ann*bnu);b=k*bw0=omegap,omegas;h,w=freqs(b,a);hx=freqs(b,a,w0);dbhx=-20*log10(abs(hx)/max(abs(h)plot(w/(2*pi)/1000,20*log10(abs(h);xlabel(f(khz);ylabel(db);axis(-1,12,-55,1);set(gca,xtickmode,manual,xtick,0,1,2,3,4,5,6,7,8,9);se

10、t(gca,ytickmode,manual,ytick,-50,-40,-30,-20,-10,0);grid;显示结果如下图：6 设计一线性相位fir数字滤波器截止频率wc=0.2,过滤带宽度w40db,用hanning汉宁窗、hamming汉明窗以及blackman窗设计（可以查阅相关表格），并用matlab软件实现（包括画图）。解：查资料有如下表1 各种窗函数的基本参数窗函数旁瓣峰值幅度/db过渡带宽阻带最小衰减/db矩形窗-134/n-12三角形窗-258/n-25汉宁窗-318/n-44哈明窗-418/n-53布莱克窗-5712/n-74凯塞窗（=7.865）-5710/n-80由

11、上表并经计算可知n的取值为n=20表2 不同的值对应的凯塞窗过渡带宽b/rad阻带最小衰减/db2.2103.00303.3844,46404.5385.86505.6587.24606.76412.870由表可知=3.384则用matlab软件仿真的程序如下：clc;clear all;n=20;n=1:n;beta=3.384;wdhn=hanning(n);wdhm=hamming(n);wdbl=blackman(n);wdks=kaiser(n,beta);plot(n,wdhn,wdhm,wdbl,wdks)legend(hn,hm,bl,ks)仿真的结果如下图：7 用kaiser窗设计满足下列指标的相位fir低通滤波器，要求wp=0.3,wc=0.5,ap=1db,ac=40db 解：设计kaiser窗满足题意，利用matlab软件可先求出窗口的介数以及的值，经计算可知n=25，=3.4493 利用matlab软件求值的程序如下： clc;clear all;wp=0.3*pi;ws=0.5*pi;as=40;deltaf=(ws-wp)/(2*pi);n0=ceil(as-7.95)/(14.36