Matlab实现数字FIR的高通带通低通带阻滤波器的解析Word文件下载.docx
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f=[00.60.71];
%给定频率轴分点
A=[1100];
%给定在这些频率分点上理想的幅频响应
weigh=[110];
%给定在这些频率分点上的加权
b=remez(32,f,A,weigh;
%设计出切比雪夫最佳一致逼近滤波器[h,w]=freqz(b,1,256,1;
h=abs(h;
h=20*log10(h;
subplot(211
stem(b,'
.'
grid;
切比雪夫逼近滤波器的抽样值'
subplot(212
plot(w,h;
滤波器幅频特性(dB'
利用汉宁窗设计Ⅰ型数字带阻滤波器
Wpl=0.2*pi;
Wph=0.8*pi;
Wsl=0.4*pi;
Wsh=0.6*pi;
tr_width=min((Wsl-Wpl,(Wph-Wsh;
Wcl=(Wsl+Wpl/2;
Wch=(Wsh+Wph/2;
hd=ideal_bs(Wcl,Wch,N;
%理想低通滤波器的单位冲激响应w_hann=(hanning(N'
h=hd.*w_hann;
%截取得到实际的单位脉冲响应
[db,mag,pha,w]=freqz_m2(h,[1];
Ap=-(min(db(1:
Wpl/delta_w+1%实际通带纹波
As=-round(max(db(Wsl/delta_w+1:
Wsh/delta_w+1%实际阻带纹波
stem(n,w_hann
利用三角窗设计Ⅲ型数字带通滤波器
Wpl=0.4*pi;
Wph=0.6*pi;
Wsl=0.2*pi;
Wsh=0.8*pi;
tr_width=min((Wpl-Wsl,(Wsh-Wph;
N=ceil(6.1*pi/tr_width%滤波器长度
hd=ideal_bp2(Wcl,Wch,N;
%理想低通滤波器的单位冲激响应
w_tri=(triang(N'
%三角窗
h=hd.*w_tri;
%计算实际滤波器的幅度响应
delta_w=2*pi/1000;
Ap=-(min(db(Wpl/delta_w+1:
Wph/delta_w+1%实际通带纹波
As=-round(max(db(Wsh/delta_w+1:
501%实际阻带纹波
stem(n,w_tri
三角窗w(n'
利用布拉克曼窗设计Ⅱ型数字带通滤波器
N=ceil(11*pi/tr_width+1%滤波器长度
hd=ideal_bp1(Wcl,Wch,N;
w_bman=(blackman(N'
%布拉克曼窗
h=hd.*w_bman;
stem(n,w_bman
布拉克曼窗w(n'
利用海明窗设计Ⅱ型数字低通滤波器
Wp=0.2*pi;
tr_width=Ws-Wp;
N=ceil(6.6*pi/tr_width+1%滤波器长度
hd=ideal_lp1(Wc,N;
w_ham=(hamming(N'
%海明窗
h=hd.*w_ham;
Wp/delta_w+1%实际通带纹波
As=-round(max(db(Ws/delta_w+1:
stem(n,w_ham
海明窗w(n'
%--------------------------------------------------------
function[db,mag,pha,w]=freqz_m2(b,a
%滤波器的幅值响应(相对、绝对、相位响应
%db:
相对幅值响应
%mag:
绝对幅值响应
%pha:
相位响应
%w采样频率;
%b系统函数H(z的分子项(对FIR,b=h
%a系统函数H(z的分母项(对FIR,a=1
[H,w]=freqz(b,a,1000,'
whole'
H=(H(1:
501'
w=(w(1:
mag=abs(H;
%绝对幅值响应
db=20*log10((mag+eps/max(mag;
%相对幅值响应
pha=angle(H;
%相位响应
利用模拟Butterworth滤波器设计数字低通滤波器
%exa4-8_pulseDFforexample4-8
%usingButterworthanaloglowpassfiltertodesigndigitallowpassfilter%利用模拟Butterworth滤波器设计数字低通滤波器
%脉冲响应不变法
wp=0.2*pi;
ws=0.3*pi;
Rp=1;
As=15;
T=1;
%性能指标
Rip=10^(-Rp/20;
Atn=10^(-As/20;
OmgP=wp*T;
OmgS=ws*T;
[N,OmgC]=buttord(OmgP,OmgS,Rp,As,'
s'
%选取模拟滤波器的阶数[cs,ds]=butter(N,OmgC,'
%设计出所需的模拟低通滤波器[b,a]=impinvar(cs,ds,T;
%应用脉冲响应不变法进行转换%求得相对、绝对频响及相位、群迟延响应
[db,mag,pha,grd,w]=freqz_m(b,a;
%下面绘出各条曲线
subplot(2,2,1;
plot(w/pi,mag;
幅频特性'
xlabel('
w(/pi'
ylabel('
|H(jw|'
axis([0,1,0,1.1];
set(gca,'
XTickMode'
'
manual'
XTick'
[00.20.30.51];
YTickMode'
YTick'
[0AtnRip1];
grid
subplot(2,2,2;
plot(w/pi,db;
幅频特性(dB'
dB'
axis([0,1,-40,5];
[-40-As-Rp0];
subplot(2,2,3;
plot(w/pi,pha/pi;
相频特性'
pha(/pi'
axis([0,1,-1,1];
subplot(2,2,4;
plot(w/pi,grd;
群延迟'
Sample'
axis([0,1,0,12];
function[db,mag,pha,grd,w]=freqz_m(b,a
%滤波器幅值响应(绝对、相对、相位响应及群延迟
%Usage:
[db,mag,pha,grd,w]=freqz_m(b,a%500点对应[0,pi]
%db相对幅值响应;
mag绝对幅值响应;
pha相位响应;
grd群延迟响应
b系统函数H(z的分子项(对FIR,b=h
[H,w]=freqz(b,a,500;
%500点的复频响应
grd=grpdelay(b,a,w;
基于频域抽样法的FIR数字带阻滤波器设计
N=41;
T1=0.598;
alpha=(N-1/2;
l=0:
wl=(2*pi/N*l;
Hrs=[ones(1,6,T1,zeros(1,7,T1,ones(1,11,T1,zeros(1,7,T1,ones(1,6];
%理想振幅采样响应
Hdr=[1,1,0,0,1,1];
wdl=[0,0.3,0.3,0.7,0.7,1];
k1=0:
floor((N-1/2;
k2=floor((N-1/2+1:
angH=[pi/2-alpha*(2*pi/N*(k1+0.5,-pi/2+alpha*(2*pi/N*(N-k2-0.5];
%相位约束条件
Hdk=Hrs.*exp(j*angH;
%构成Hd(k
h1=ifft(Hdk,N;
h=real(h1.*exp(j*pi*n/N;
%实际单位冲激响应
[Hr,ww,a,L]=hr_type3(h;
%实际振幅响应
plot(wl/pi+1/N,Hrs,'
wdl,Hdr
频率样本Hd(k:
N=41'
axis([01-0.11.2]
stem(l,h
实际单位脉冲响应h(n'
plot(ww/pi,Hr,wl/pi+1/N,Hrs,'
实际振幅响应H(w'
axis([01-8010]
function[db,mag,pha,w]=freqz_m(b,a;
[H,w]=freqz(b,a,1000,'
H=(H(1:
w=(w(1:
mag=abs(H;
db=20*log10((mag+eps/max(mag;
pha=angle(H;
%pha=unwrap(angle(H;
function[Hr,w,c,L]=hr_type3(h;
%计算所设计的3型滤波器的振幅响应
%Hr=振幅响应
%b=3型滤波器的系数
%L=Hr的阶次
%h=3型滤波器的单位冲击响应
M=length(h;
L=(M-1/2;
c=[2*h(L+1:
-1:
1];
n=[0:
L];
w=[0:
500]'
*2*pi/500;
Hr=sin(w*n*c'
基于频域抽样法的FIR数字带通滤波器设计
wsl=0.12*pi;
%低阻带边缘
wsh=0.82*pi;
%高阻带边缘
wpl=0.32*pi;
%低通带边缘
wph=0.62*pi;
%高通带边缘
delta=(wpl-wsl;
%过度带
M=ceil(2*pi*3/delta;
%抽样点数
al=(M-1/2;
wl=(2*pi/M;
%抽样间隔
k=0:
M-1;
T1=0.12;
T2=0.6;
%过渡带样本点
Hrs=[zeros(1,ceil(0.12*pi/wl+1,T2,T1,ones(1,ceil(0.3*pi/wl,T1,T2,zeros(1,ceil(0.3734*pi/wl,T2,T1,ones(1,ceil(0.3*pi/wl,T1,T2,zeros(1,ceil(0.12*pi/wl+1];
wdl=[00.120.320.620.821];
floor((M-1/2;
k2=floor((M-1/2+1:
angH=[-al*(2*pi/M*k1,al*(2*pi/M*(M-k2];
H=Hrs.*exp(j*angH;
h=real(ifft(H;
%傅立叶反变换
figure(1;
%冲击响应图
stem(k,h;
impulseresponse'
n'
h(n'
figure(2;
%幅频曲线图
Hf=abs(H;
w=k*wl/pi;
plot(w,Hf,'
*b-'
axis([01-0.11.1];
amplituderesponse'
frequencyinpiunits'
Hr(w'
xtickmode'
xtick'
wdl;
ytickmode'
ytick'
[00.120.61];
grid;
figure(3;
fs=15000;
[c,f3]=freqz(h,1;
f3=f3/pi*fs/2;
plot(f3,20*log10(abs(c;
频谱特性'
频率/HZ'
衰减/dB'
t=(0:
100/fs;
x=sin(2*pi*t*700+sin(2*pi*t*3200+sin(2*pi*t*6200;
q=filter(h,1,x;
[a,f1]=freqz(x;
f1=f1/pi*fs/2;
[b,f2]=freqz(q;
f2=f2/pi*fs/2;
figure(4;
subplot(2,1,1;
plot(f1,abs(a;
输入波形频谱图'
频率'
幅度'
subplot(2,1,2;
plot(f2,abs(b;
输出波形频谱图'
基于汉宁窗的FIR数字高通滤波器设计
functions2
Fs=15000;
100/Fs;
x=sin(2*pi*500*t+sin(2*pi*3000*t
subplot(245;
stem(x;
原始信号'
axis([0,100,-2,2];
Ws=7*pi/30;
Wp=13*pi/30;
tr_wid=Wp-Ws;
N=ceil(11*pi/tr_wid%滤波器长度
%理想高通滤波器的截止频率
%理想高通滤波器的单位冲激响应w_bla=(blackman(N'
%布拉克曼
h=hd.*w_bla;
%截取得到实际的单位脉冲响应[db,mag,pha,grd,w]=freqz_m(h,[1];
Ws/delta_w+1%实际阻带纹波,round是取整函数y=filter(h,1,x
subplot(246
plot(y
滤波后的信号'
axis([0,100,-1,1]
subplot(241
subplot(242
stem(n,w_bla
布拉克满窗w(n'
subplot(243
subplot(244
function[db,mag,pha,grd,w]=freqz_m(b,a;
grd=grpdelay(b,a,w;
subplot(247;
plot(phatitle('
相频响应'
functionhd=ideal_hp1(Wc,Nalp=(N-1/2;
n=0:
m=n-alp+eps;
%eps是一个很小很小的数hd=[sin(pi*m-sin(Wc*m]./(pi*m;
用双线性法设计巴特沃斯高通数字滤波器clearall;
clc;
closeallfs=120;
T=1/fs;
rp=1;
rs=30;
Wp=0.35*pi;
Ws=0.65*pi;
%数字滤波器指标wp=2*tan(Wp/2/T;
ws=2*tan(Ws/2/T;
%预畸变,将数字滤波器的指标变为模拟滤波器的指标[N,w]=buttord(wp,ws,rp,rs,'
%求滤波器阶数和3dB截止频率[Z,P,K]=buttap(N;
%设计模拟低通滤波器[Md,Nd]=zp2tf(Z,P,K;
%将零极点形式转换为传输函数形式[M