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%由于用freqz计算频点至少是2个，所以至少输入两个频点
w1=input（'
请输入你要计算的频点w1='
w2=input（'
请输入你要计算的频点w2='
w=[w1w2];
num=[25953];
den=[545211];
h=freqz（num,den,w）
（6）WriteaMATLABprogramtocomputeandplotthemagnituderesponseofacausalLTIdiscrete-timesystemwithatransferfunctiongivenby
num=0.15*[10-1];
den=[1-0.50.7];
[h,w]=freqz（num,den,512）;
plot（w/pi,abs（h））
（7）ConsiderthefollowingFIRtransferfunction:
UsingMATLABtodetermineitszerolocationsandplotitsmagnitudeandphaseresponse.
h=[10.6.49-0.48-0.14-0.120.09];
figure
（1）
zplane（h,1）;
[H,w]=freqz（h,1,512）;
figure
（2）
plot（w/pi,abs（H））
figure（3）
plot（w/pi,angle（H））
（8）Givenasignal
whenusingasamplingfrequencyfT=20KHz,plotthemagnitudeandphasespectrumofthesampledsequence（givenlength-64）.
fs=2e4;
n=（0:
63）/fs;
x=4*n+cos（0.1*pi*n）;
h=fft（x,512）;
2/511:
2,abs（h））
2,angle（h））
（9）designanIIRbutterworthdigitallowpassfilterwiththefollowingspecifications:
samplingrate
of40kHz,passbandedgefrequencyof4kHz,stopbandedgefrequencyof8kHz,passbandrippleof0.5dB,andaminimumstopbandattenuationof40dB,plotfrequency-magnitudeandcheckifyourdesignfitsthespecification.
fs=40;
wp=4*2/fs;
ws=8*2/fs;
ap=0.5;
as=40;
[n,wn]=buttord（wp,ws,ap,as）;
[num,den]=butter（n,wn）;
plot（w/pi,20*log10（abs（h）））
axis（[01-500]）
axis（[0wp-0.50]）;
title（'
通带纹波'
）
axis（[ws1-50-30]）
阻带纹波'
（10）DesignaHanningFIRlowpassfiltermeetingthefollowingspecifications:
passbandedgefrequency=2kHz,stopbandedgefrequency=2.5kHz,passbandrippleδp=0.005,stopbandrippleδs=0.005,andsamplingrateof10kHz.Plotitsgainandphaseresponsesandcheckifitmeetsthespecifications?
ft=10;
fp=2;
fs=2.5;
wp=2*pi*fp/ft;
ws=2*pi*fs/ft;
ds=0.005;
ap=20*log10（1-ds）;
as=20*log10（ds）
wc=（wp+ws）/2;
dw=ws-wp;
M=ceil（3.11*pi/dw）;
N=2*M;
b=fir1（N,wc/pi,hann（N+1））;
[h,w]=freqz（b,1,512）;
plot（w/pi,20*log10（abs（h）））;
magituderesponse'
plot（w/pi,unwrap（angle（h）））;
phaseresponse'
axis（[0wp/piap0]）
axis（[ws/pi1as0]）
%从图中可以看出，通带和阻带中纹波都不满足要求，所以不满足指标
%as=-46.0206<
43.9所以不能用hanning窗设计
%应当用hamming或blackman窗设计
1.DFT定义，矩阵形式运算，循环运算1
2.fir1,kaiserord,Kaiser,freqz2
3.cheb1ord,cheb12
4.系统函数的二阶分解，tf2sos,tf2zp,sort,unique3
5.零极点形式到直接型的转换3
6.阶数估计（表10.2）,hann,fir1，根据定义加窗4
7.freqz,real,imag,abs,angle,unwrap,phase4
8.fir1,hamming窗5
9.直接型转零极点型，tf2zp6
10.butter,buttord6
11.部分分式展开（逆），从传输函数计算冲击响应，residuez,impz7
12.freqz,real,imag,abs,phase,angle,unwrap7
13.ellipord,ellip,freqz8
14.fir1,hann,分贝转换9
15.信号能量计算9
16.各IIR阶数估计，buttord,cheb1ord,cheb2ord,ellipord9
17.square,freqz10
18.线性卷积，此处用fft实现11
19.圆周卷积，要求用基于DFT的方法实现11
20.部分分式展开，逆z变换，residuez12
21.freqz13
22.信号通过系统的输出，filter13
23.信号通过系统的输出，filter13
24.重要提示14
1.DFT定义，矩阵形式运算，循环运算
%WritingaMATLABprogramtocompute128-pointDFTof
%thefollowingsequence,youmustfirstlyuse
%DFTdefinition（directlycomputingDFT）tocompute
%anduseMATLABfunctiontotesttheresult.
%Plotthetworesultsinonefigure.
%g[n]=sin（pi*n/4）,0<
=n<
=31
N=32;
M=128;
n=0:
（N-1）;
m=0:
（M-1）;
g=sin（pi*n/4）;
%DFTdefinition%matrixexpressionofDFT
G1=g*exp（-2*j*pi/M）.^（n'
*m）;
%followingisthedirectconversion
%fromdefinitiontocode
%forii=0:
M-1
%G1（ii+1）=0;
%forjj=0:
N-1
%G1（ii+1）=G1（ii+1）+g（jj+1）*exp（-2*j*pi/M*ii*jj）;
%end
%endsubplot（2,1,1）;
plot（m,abs（G1））;
%fftrealizedbyMATLAB
G2=fft（g,M）;
subplot（2,1,2）;
plot（m,abs（G2））;
2.fir1,kaiserord,Kaiser,freqz
%Usingthefunctionfir1andwindowofKaiser,
%designalinear-phaseFIRlowpassfilter
%meetingthefollowingspecifications:
%passbandedgefrequency=2kHz,
%stopbandedgefrequency=2.5kHz,
%passbandrippleδp=0.005,
%stopbandrippleδs=0.005,
%andsamplingrateof10kHz.
%Plotitsgainandphaseresponses
%andcheckifitmeetsthespecifications?
fsamp=10000;
fcuts=[20002500];
mags=[10];
devs=[0.0050.005];
[n,Wn,beta,ftype]=kaiserord（fcuts,mags,devs,fsamp）;
hh=fir1（n,Wn,kaiser（n+1,beta）,'
noscale'
freqz（hh）
3.cheb1ord,cheb1
%DesignaType1ChebyshevIIRlowpassfiltermeeting
%thespecificationsasbelow:
%samplingrateof12kHz,
%passbandedgefrequencyof2.1kHz,
%stopbandedgefrequencyof2.7kHz,
%passbandrippleof0.6dB,
%andaminimumstopbandattenuationof45dB.
%Writedowntheexactexpressionfor
%thetransferfunctiongenerated.
%Doesyourdesignmeetthespecifications?
Fs=12000;
Fn=Fs/2;
%Nyquistcriterion
Wp=2100/Fn;
Ws=2700/Fn;
Rp=0.6;
Rs=45;
[n,Wn]=cheb1ord（Wp,Ws,Rp,Rs）
[b,a]=cheby1（n,Rp,Wn）
freqz（b,a,512,Fs）;
%b=
%0.00010.00090.00320.0064...
%0.00800.00640.00320.00090.0001
%a=
%1.0000-4.681811.1095-16.8220...
%17.5480-12.83006.4101-2.00620.3038
4.系统函数的二阶分解，tf2sos,tf2zp,sort,unique
%UsingMATLABdeterminethesecond-orderfactoredform
%ofthefollowingz-transforms.Andshowtheirpole-zeroplots.
%ThendetermineallpossibleROCsofabovez-transform.
%4*z^4+15.6*z^3+6*z^2+2.4*z-6.4
%G1（z）=-----------------------------------------------
%3*z^4+2.4*z^3+6.3*z^2-11.4*z+6
num=[4,15.6,6,2.4,-6.4];
den=[3,2.4,6.3,-11.4,6];
[sosg]=tf2sos（num,den）
[zpk]=tf2zp（num,den）;
pp=sort（unique（[0,abs（p）'
inf]））;
forii=1:
length（pp）-1
fprintf（'
possibleROC%d:
（%f,%f）\n'
ii,pp（ii）,pp（ii+1））;
end
5.零极点形式到直接型的转换
%WriteaMATLABprogramtocomputeanddisplay
%therationalz-transformfromitszero,
%polesandgainconstant.IftheDTFTof
%thecausalsystemexists,trytoplot
%it'
smagnitudeandphasespectra.
%Usingthisprogramtodeterminetherationalform
%ofaz-transformwhosezeroareat
%ξ1=1.2,ξ2=2.3-j0.5,ξ3=-0.4+j0.2,ξ4=-0.4-j0.2,ξ5=2.3+j0.5;
%theploesareat
%λ1=0.5,λ2=-0.75+j0.2,λ3=0.6+j0.7,λ4=0.6-j0.7,λ5=-0.75-j0.2;
%andthegainconstantkis2.1.functionmainz=[1.2,2.3-j*0.5,-0.4+j*0.2,-0.4-j*0.2,2.3+j*0.5];
p=[0.5,-0.75,+j*0.2,0.6+j*0.7,0.6-j*0.7,-0.75-j*0.2];
k=2.1;
rzt（z,p,k）;
return;
functionrzt（z,p,k）
%computeanddisplay
num=k*poly（z）
den=poly（p）
freqz（num,den）;
6.阶数估计（表10.2）,hann,fir1，根据定义加窗
%DesignanFIRhanningdigitallowpassfilter
%withthefollowingspecifications:
%passbandedgefrequency0.3*pi,
%stopbandedgefrequency0.4*pi,
%stopbandattenuation40dB.
%Pleaseplotfrequency-magnitituderesponse
%andcheckifyourdesignfitthespecification。
wp=0.3*pi;
ws=0.4*pi;
wn=（wp+ws）/2;
rs=40;
%choosehanningwindowaccordingtotable10.2%basicparameter
dw=ws-wp;
M=ceil（3.11*pi/dw）;
N=M*2;
%lengthis（N+1）%designusingfir1
h=fir1（N,wn/pi,hann（N+1））;
freqz（h,1）;
figure;
%designaccordingtoCHAP10
wc=（wp+ws）/2;
n=-M:
M;
hd=wc/pi*sinc（n*wc/pi）;
w=0.5+0.5*cos（2*pi*n/（N+1））;
ht=hd.*w;
freqz（ht,1）;
7.freqz,real,imag,abs,angle,unwrap,phase
%Givenasignal
%x（t）=sin（0.1*pi*t）+2*cos（0.3*pi*t）+3*sin（0.5*pi*t）
%whenusingasamplingfrequencyfT=20KHz,
%plotthemagnitudeandphasespectrumofthesampledsequence
%（givenlength-64）.
N=64;
fT=20*1000;
N-1;
t=n/fT;
x=sin（0.1*pi*t）+2*cos（0.3*pi*t）+3*sin（0.5*pi*t）;
[hw]=freqz（x,1）;
subplot（2,1,1）;
plot（w,abs（h））;
Magnitude'
）;
xlabel（'
\omega/\pi'
ylabel（'
plot（w,angle（h））;
%angle（）wraptheresultsto[-pi,pi]
Phase'
8.fir1,hamming窗
%Usingthefunctionfir1andwindowofHamming,
%stopbandedgefrequency=2.3kHz,
%passbandrippleδp=0.002,
%stopbandrippleδs=0.002
%andsamplingrateof20kHz.
rp=0.002;
%thetwoparameterisonlyusedto
%determinewhichwindowtochoose
%accordingtotable10.2
rs=0.002;
%=26.9897dB,hammingwindowcandofp=2*1000;
fs=2.3*100
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