长沙理工数字信号处理大作业数字滤波器设计.docx
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长沙理工数字信号处理大作业数字滤波器设计.docx
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长沙理工数字信号处理大作业数字滤波器设计
IIR及FIR数字滤波器
一题干
对模拟信号进行低通滤波处理,要求通带0≤f≤4kHz,通带衰减小于0.5dB,阻带4.5kHz≤f<∞,阻带衰减大于50dB,设采样频率Fs=20kHz。
(1)设计巴特沃斯模拟低通滤波器,求出Ha(s)的分子、分母多项式系数B和A,并画出幅频响应损耗函数曲线。
(2)分别用脉冲响应不变法和双线性变换法设计IIR低通数字滤波器,求出Ha(z)的分子、分母多项式系数Bz和Az,并画出幅频响应损耗函数曲线
(3)采用窗函数法(分别用汉宁窗、哈明窗、布莱克曼窗函数)设计满足要求的FIR低通滤波器,求出h(n),并画出幅频响应损耗函数曲线.
(4)用频率采样法设计满足要求的FIR低通滤波器,求出h(n),并画出幅频响应损耗函数曲线。
二求解过程
具体内容如下:
(1)设计巴特沃斯模拟低通滤波器,求出Ha(s)的分子、分母多项式系数B和A,并画出幅频响应损耗函数曲线。
程序:
wp=2*pi*4000;
ws=2*pi*5800;
Rp=0.5;
As=50;
[N,wc]=buttord(wp,ws,Rp,As,'s');
[B,A]=butter(N,wc,'s');
k=0:
511;
fk=0:
20000/512:
20000;
wk=2*pi*fk;
Hk=freqs(B,A,wk);
plot(fk/1000,20*log10(abs(Hk)));
gridon
xlabel('频率/kHz');
ylabel('幅度/dB');
axis([0,6,-65,5]);
波形图:
A=1.0e+207*
0.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00202.1576
B=1.0e+207*
00000000000000000000000000000000000000000000002.1576
N=46
(2)分别用脉冲响应不变法和双线性变换法设计IIR低通数字滤波器,求出Ha(z)的分子、分母多项式系数Bz和Az,并画出幅频响应损耗函数曲线
脉冲响应不变法
程序:
Fs=20000;
wp=10000*pi;
ws=11600*pi;
Rp=0.5;
As=50;
[N,wc]=buttord(wp,ws,Rp,As,'s');
[B,A]=butter(N,wc,'s');
[Bz,Az]=impinvar(B,A);
k=0:
511;
fk=0:
20000/512:
20000;
wk=2*pi*fk;
Hk=freqs(B,A,wk);
plot(fk/1000,20*log10(abs(Hk)));
gridon;
xlabel('频率/kHz');
ylabel('幅值/dB');
axis([0,6,-65,5]);
波形图:
Bz=1.0e-007*
0-0.00000.0000-0.00000.0001-0.00060.0035-0.01160.0279-0.07450.1490-0.22350.3353-0.37250.4470-0.40980.3353-0.22350.1304-0.06980.0291-0.00930.0026-0.00060.0001-0.00000.0000-0.0000
Az=1.0e+007*
0.0000-0.00000.0000-0.00030.0018-0.00810.0296-0.08880.2219-0.46840.8431-1.30281.7370-2.00412.0040-1.73671.3024-0.84270.4681-0.22170.0887-0.02960.0081-0.00180.0003-0.00000.0000-0.0000
N=46
双线性变换法
程序:
Fs=20000;wpz=10000/Fs;
wsz=11600/Fs;
Rp=0.5;
As=50;
wp=2*tan(wpz*pi/2);
ws=2*tan(wsz*pi/2);[N,wc]=buttord(wp,ws,Rp,As,'s');[B,A]=butter(N,wc,'s');[Bz,Az]=bilinear(B,A,Fs);
[Nd,wdc]=buttord(wpz,wsz,Rp,As);
[Bdz,Adz]=butter(Nd,wdc);
k=0:
511;
fk=0:
20000/512:
20000;
wk=2*pi*fk;Hk=freqs(B,A,wk);plot(fk/1000,20*log10(abs(Hk)));
gridon;xlabel('频率/kHz');
ylabel('幅值/dB');axis([0,16,-2800,5])
波形图:
Bz=1.0e-007*
0-0.00000.0000-0.00000.0001-0.00060.0035-0.01160.0279-0.07450.1490-0.22350.3353-0.37250.4470-0.40980.3353-0.22350.1304-0.06980.0291-0.00930.0026-0.00060.0001-0.00000.0000-0.0000
Az=1.0e+007*
0.0000-0.00000.0000-0.00030.0018-0.00810.0296-0.08880.2219-0.46840.8431-1.30281.7370-2.00412.0040-1.73671.3024-0.84270.4681-0.22170.0887-0.02960.0081-0.00180.0003-0.00000.0000-0.0000
N=27
(3)采用窗函数法(分别用汉宁窗、哈明窗、布莱克曼窗函数)设计满足要求的FIR低通滤波器,求出h(n),并画出幅频响应损耗函数曲线.
a)汉宁窗
程序:
Fs=20000;
fp=4000;
fs=5800;
m=[1100];
wp=2*pi*fp/Fs;
ws=2*pi*fs/Fs;
Rp=0.5;
As=50;
Bt=ws-wp;
N0=ceil(6.6*pi/Bt);
N=N0+mod(N0+1,2);
wc=(wp+ws)/2/pi;
hn=fir1(N-1,wc,hanning(N));
freqz(hn,1,512);
plot(w,20*log(abs(hn)));
grid;
axis([0,1,-1000,100]);
xlabel('频率/kHz');
ylabel('幅值/dB');
波形图:
hn=
0.0000-0.0000-0.00000.0002-0.0000-0.00040.00020.0007-0.0006-0.00100.00120.0012-0.0021-0.00100.00320.0005-0.00450.00060.0057-0.0025-0.00660.00500.0070-0.0083-0.00650.01230.0047-0.0168-0.00120.0215-0.0046-0.02620.01340.0307-0.0270-0.03450.04970.0375-0.0974-0.03940.31540.54000.3154-0.0394-0.09740.03750.0497-0.0345-0.02700.03070.0134-0.0262-0.00460.0215-0.0012-0.01680.00470.0123-0.0065-0.00830.00700.0050-0.0066-0.00250.00570.0006-0.00450.00050.0032-0.0010-0.00210.00120.0012-0.0010-0.00060.00070.0002-0.0004-0.00000.0002-0.0000-0.00000.0000
b)哈明窗
程序:
Fs=20000;
fp=4000;
fs=5800;
m=[1100];
wp=2*pi*fp/Fs;
ws=2*pi*fs/Fs;
Rp=0.5;
Rs=50;
Bt=ws-wp;
N0=ceil(6.6*pi/Bt);
N=N0+mod(N0+1,2);
wc=(wp+ws)/2/pi;
hn=fir1(N-1,wc,hamming(N));
freqz(hn,1,512);
plot(w,20*log(abs(hn)));
gridon;
axis([0,1,-1000,100]);
xlabel('频率/kHz');
ylabel('幅值/dB');
波形图:
hn=
0.0003-0.0006-0.00010.0008-0.0001-0.00100.00040.0012-0.0008-0.00140.00160.0015-0.0025-0.00120.00370.0005-0.00490.00070.0061-0.0026-0.00690.00520.0072-0.0086-0.00660.01250.0048-0.0170-0.00120.0217-0.0046-0.02640.01350.0308-0.0271-0.03460.04980.0375-0.0975-0.03940.31540.54010.3154-0.0394-0.09750.03750.0498-0.0346-0.02710.03080.0135-0.0264-0.00460.0217-0.0012-0.01700.00480.0125-0.0066-0.00860.00720.0052-0.0069-0.00260.00610.0007-0.00490.00050.0037-0.0012-0.00250.00150.0016-0.0014-0.00080.00120.0004-0.0010-0.00010.0008-0.0001-0.00060.0003
c)布莱克曼窗
程序:
Fs=20000;
fp=4000;
fs=5800;
m=[1100];
wp=2*pi*fp/Fs;
ws=2*pi*fs/Fs;
Rp=0.5;
Rs=50;
Bt=ws-wp;
N0=ceil(6.6*pi/Bt);
N=N0+mod(N0+1,2);
wc=(wp+ws)/2/pi;
hn=fir1(N-1,wc,blackman(N));
freqz(hn,1,512);
plot(w,20*log(abs(hn)));
grid;
axis([0,1,-1000,100]);
xlabel('频率/kHz');
ylabel('幅值/dB');
波形图:
hn=
-0.0000-0.0000-0.00000.0000-0.0000-0.00010.00010.0002-0.0002-0.00040.00050.0005-0.0009-0.00050.00160.0002-0.00240.00040.0034-0.0015-0.00430.00340.0049-0.0060-0.00490.00950.0037-0.0137-0.00100.0186-0.0040-0.02370.01240.0288-0.0257-0.03330.04850.0369-0.0965-0.03920.31500.54000.3150-0.0392-0.09650.03690.0485-0.0333-0.02570.02880.0124-0.0237-0.00400.0186-0.0010-0.01370.00370.0095-0.0049-0.00600.00490.0034-0.0043-0.00150.00340.0004-0.00240.00020.0016-0.0005-0.00090.00050.0005-0.0004-0.00020.00020.0001-0.0001-0.00000.0000-0.0000-0.0000-0.0000
(4)用频率采样法设计满足要求的FIR低通滤波器,求出h(n),并画出幅频响应损耗函数曲线。
程序:
T=input('T=')
fp=4000;
fs=5800;
Fs=20000;
wp=2*pi*fp/Fs;
ws=2*pi*fs/Fs;
Rp=0.5;
As=50;
Bt=ws-wp;
m=1;
N=ceil((m+1)*2*pi/Bt);
N=N+mod(N+1,2);
Np=fix(wp/(2*pi/N));
Ns=N-2*Np-1;
Hk=[ones(1,Np+1),zeros(1,Ns),ones(1,Np)];
Hk(Np+2)=T;
Ak(N-Np)=T;
thetak=-pi*(N-1)*(0:
N-1)/N;
hdk=Hk.*exp(j*thetak);
hn=real(ifft(hdk));
hw=fft(hn,1024);
wk=2*pi*[0:
1023]/1024;
hgw=hw.*exp(j*wk*(N-1)/2);
Rp=max(20*log10(abs(hgw)));
hgmin=min(real(hgw));
As=20*log10(abs(hgmin));
[N,wc]=buttord(wp,ws,Rp,As,'s');
[B,A]=butter(N,wc,'s');
k=0:
511;fk=0:
20000/512:
20000;wk=2*pi*fk;
Hk=freqs(B,A,wk);
plot(fk/1000,20*log10(abs(Hk)));
gridon;
xlabel('频率/kHz');
ylabel('幅度/dB');
T=1
T=
1
Rp=
0.2801
As=
-29.6745
波形图:
hn=
0.00040.0012-0.0023-0.00270.00450.0040-0.0069-0.00510.00980.0061-0.0133-0.00700.01750.0078-0.0230-0.00840.03050.0089-0.0416-0.00930.06090.0096-0.1044-0.00970.31780.50980.3178-0.0097-0.10440.00960.0609-0.0093-0.04160.00890.0305-0.0084-0.02300.00780.0175-0.0070-0.01330.00610.0098-0.0051-0.00690.00400.0045-0.0027-0.00230.00120.0004
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