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<信號(hào)與系統(tǒng)MATLAB實(shí)踐> 練習(xí)一 實(shí)驗(yàn)一 二. 熟悉簡(jiǎn)單的矩陣輸入 1.實(shí)驗(yàn)代碼 >>A=[1,2,3;4,5,6;7,8,9] 實(shí)驗(yàn)結(jié)果 A = 1 2 3 4 5 6 7 8 9 3．實(shí)驗(yàn)代碼 >>B=[9,8,7;6,5,4;3,2,1] C=[4,5,6;7,8,9;1,2,3] 實(shí)驗(yàn)結(jié)果： B = 9 8 7 6 5 4 3 2 1 C = 4 5 6 7 8 9 1 2 3 4．>> A A = 1 2 3 4 5 6 7 8 9 >> B B = 9 8 7 6 5 4 3 2 1 >> C C = 4 5 6 7 8 9 1 2 3 三. 基本序列運(yùn)算 1.>>A=[1,2,3],B=[4,5,6] A = 1 2 3 B = 4 5 6 >> C=A+B C = 5 7 9 >> D=A-B D = -3 -3 -3 >> E=A.*B E = 4 10 18 >> F=A./B F = 0.2500 0.4000 0.5000 >> G=A.^B G = 1 32 729 >> stem(A) >> stem(B) >> stem(C) >> stem(D) >> stem(E) >> stem(F) >> stem(G) 再舉例: >> a=[-1,-2,-3] a = -1 -2 -3 >> b=[-4,-5,-6] b = -4 -5 -6 >> c=a+b c = -5 -7 -9 >> d=a-b d = 3 3 3 >> e=a.*b e = 4 10 18 >> f=a./b f = 0.2500 0.4000 0.5000 >> g=a.^b g = 1.0000 -0.0313 0.0014 >> stem(a) >> stem(b) >> stem(c) >> stem(d) >> stem(e) >> stem(f) >> stem(g) 2. >>t=0:0.001:10 f=5*exp(-t)+3*exp(-2*t); plot(t,f) ylabel('f(t)'); xlabel('t'); title('(1)'); >> t=0:0.001:3; f=(sin(3*t))./(3*t); plot(t,f) ylabel('f(t)'); xlabel('t'); title('(2)'); >> k=0:1:4; f=exp(k); stem(f) 四. 利用MATLAB求解線性方程組 2. >>A=[1,1,1;1,-2,1;1,2,3] b=[2;-1;-1] x=inv(A)*b A = 1 1 1 1 -2 1 1 2 3 b = 2 -1 -1 x = 3.0000 1.0000 -2.0000 4. >> A=[2,3,-1;3,-2,1;1,2,1] b=[18;8;24] x=inv(A)*b A = 2 3 -1 3 -2 1 1 2 1 b = 18 8 24 x = 4 6 8 實(shí)驗(yàn)二 二. 1. >> k=0:50 x=sin(k); stem(x) xlabel('k'); ylabel('sinX'); title('sin(k)ε(k)'); 2. >> k=-25:1:25 x=sin(k)+sin(pi*k); stem(k,x) xlabel('k'); ylabel('f(k)'); title('sink+sinπk'); 3. >> k=3:50 x=k.*sin(k); stem(k,x) xlabel('k'); ylabel('f(k)'); title('ksinkε(k-3)'); 4. %函數(shù) function y=f1(k) if k<0 y=(-1)^k; else y=(-1)^k+(0.5)^k; end %運(yùn)行代碼 for k=-10:1:10; y4(k+11)=f1(k); end k=-10:1:10; stem(k,y4); xlabel('k'); ylabel('f(k)'); title('4'); 七． 2．>> f1=[1 1 1 1]; f2=[3 2 1]; conv(f1,f2) ans = 3 5 6 6 3 1 3. 函數(shù)定義： function [r]= pulse( k ) if k<0 r=0; else r=1; end end 運(yùn)行代碼 for k=1:10 f1(k)=pulse(k); f2(k)=(0.5^k)*pulse(k); end conv(f1,f2) 結(jié)果 ans = Columns 1 through 10 0.5000 0.7500 0.8750 0.9375 0.9688 0.9844 0.9922 0.9961 0.9980 0.9990 Columns 11 through 20 0.9995 0.9998 0.9999 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 Columns 21 through 30 0.5000 0.2500 0.1250 0.0625 0.0312 0.0156 0.0078 0.0039 0.0020 0.0010 Columns 31 through 39 0.0005 0.0002 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 4 for i=1:10 f1(i)=pulse(i); f2(i)=((-0.5)^i)*pulse(i); end conv(f1,f2) 結(jié)果 ans = Columns 1 through 10 -0.5000 -0.2500 -0.3750 -0.3125 -0.3438 -0.3281 -0.3359 -0.3320 -0.3340 -0.3330 Columns 11 through 20 -0.3325 -0.3323 -0.3322 -0.3321 -0.3321 -0.3320 -0.3320 -0.3320 -0.3320 -0.3320 Columns 21 through 30 0.1680 -0.0820 0.0430 -0.0195 0.0117 -0.0039 0.0039 -0.0000 0.0020 0.0010 Columns 31 through 39 0.0005 0.0002 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 實(shí)驗(yàn)三 2． clear; x=[1,2,3,4,5,6,6,5,4,3,2,1]; N=0:11; w=-pi:0.01:pi; m=length(x); n=length(w); for i=1:n F(i)=0; for k=1:m F(i)=F(i)+x(k)*exp(-1j*w(i)*k); end end F=F/10; subplot(2,1,1); plot(w,abs(F),'b-');xlabel('w');ylabel('F');title('幅度頻譜');grid subplot(2,1,2); plot(w,angle(F),'b-');xlabel('w'); X=fftshift(fft(x))/10; subplot(2,1,1); hold on; plot(N*2*pi/12-pi,abs(X),'r.'); legend('DIFT算法','DFT算法'); subplot(2,1,2);hold on; plot(N*2*pi/12-pi,angle(X),'r.'); xlabel('w');ylabel('相位');title('相位頻譜');grid 三． 1. %fun1.m function y=fun1(x) if((-pi-1 y=cos(pi*x/2); else y=0; end %new2.m for i=1:1000 g(i)=fun2(2/1000*i-1); w(i)=(i-1)*0.2*pi; end for i=1001:10000 g(i)=0; w(i)=(i-1)*0.2*pi; end G=fft(g)/1000; subplot(1,2,1); plot(w(1:50),abs(G(1:50))); xlabel('w');ylabel('G');title('幅度頻譜'); subplot(1,2,2); plot(w(1:50),angle(G(1:50))) xlabel('w');ylabel('Fi');title('相位頻譜'); 3. %fun3.m function y=fun3(x) if x<0 && x>-1 y=1; elseif x>0 && x<1 y=-1; else y=0 end %new.m for i=1:1000 g(i)=fun3(2/1000*i-1); w(i)=(i-1)*0.2*pi; end for i=1001:10000 g(i)=0; w(i)=(i-1)*0.2*pi; end G=fft(g)/1000; subplot(1,2,1); plot(w(1:50),abs(G(1:50))); xlabel('w');ylabel('G');title('DFT幅度頻譜'); subplot(1,2,2); plot(w(1:50),angle(G(1:50))) xlabel('w');ylabel('Fi');title('DFT相位頻譜'); 練習(xí)二 實(shí)驗(yàn)六 一．用MATLAB語(yǔ)言描述下列系統(tǒng)，并求出極零點(diǎn)、 1. >> Ns=[1]; Ds=[1,1]; sys1=tf(Ns,Ds) 實(shí)驗(yàn)結(jié)果： sys1 = 1 ----- s + 1 >> [z,p,k]=tf2zp([1],[1,1]) z = Empty matrix: 0-by-1 p = -1 k = 1 2. >>Ns=[10] Ds=[1,-5,0] sys2=tf(Ns,Ds) 實(shí)驗(yàn)結(jié)果： Ns = 10 Ds = 1 -5 0 sys2 = 10 --------- s^2 - 5 s >>[z,p,k]=tf2zp([10],[1,-5,0]) z = Empty matrix: 0-by-1 p = 0 5 k = 10 二．已知系統(tǒng)的系統(tǒng)函數(shù)如下，用MATLAB描述下列系統(tǒng)。 1． >> z=[0]; p=[-1,-4]; k=1; sys1=zpk(z,p,k) 實(shí)驗(yàn)結(jié)果： sys1 = s ----------- (s+1) (s+4) Continuous-time zero/pole/gain model. 2. >> Ns=[1,1] Ds=[1,0,-1] sys2=tf(Ns,Ds) 實(shí)驗(yàn)結(jié)果： Ns = 1 1 Ds = 1 0 -1 sys2 = s + 1 ------- s^2 - 1 Continuous-time transfer function. 3． >> Ns=[1,6,6,0]; Ds=[1,6,8]; sys3=tf(Ns,Ds) 實(shí)驗(yàn)結(jié)果： Ns = 1 6 6 0 Ds = 1 6 8 sys3 = s^3 + 6 s^2 + 6 s ----------------- s^2 + 6 s + 8 Continuous-time transfer function. 六．已知下列H(s)或H(z)，請(qǐng)分別畫(huà)出其直角坐標(biāo)系下的頻率特性曲線。 1. >> clear; for n = 1:400 w(n) = (n-1)*0.05; H(n) = (1j*w(n))/(1j*w(n)+1); end mag = abs(H); phase = angle(H); subplot(2,1,1) plot(w,mag);title('幅頻特性') subplot(2,1,2) plot(w,phase);title('相頻特性') 實(shí)驗(yàn)結(jié)果： 2. >> clear; for n = 1:400 w(n) = (n-1)*0.05; H(n) = (2*j*w(n))/((1j*w(n))^2+sqrt(2)*j*w(n)+1); end mag = abs(H); phase = angle(H); subplot(2,1,1) plot(w,mag);title('幅頻特性') subplot(2,1,2) plot(w,phase);title('相頻特性') 實(shí)驗(yàn)結(jié)果： 3. >>clear; for n = 1:400 w(n) = (n-1)*0.05; H(n) = (1j*w(n)+1)^2/((1j*w(n))^2+0.61); end mag = abs(H); phase = angle(H); subplot(2,1,1) plot(w,mag);title('幅頻特性') subplot(2,1,2) plot(w,phase);title('相頻特性') 實(shí)驗(yàn)結(jié)果： 4. >>clear; for n = 1:400 w(n) = (n-1)*0.05; H(n) =3*(1j*w(n)-1)*(1j*w(n)-2)/(1j*w(n)+1)*(1j*w(n)+2); end mag = abs(H); phase = angle(H); subplot(2,1,1) plot(w,mag);title('幅頻特性') subplot(2,1,2) plot(w,phase);title('相頻特性') 實(shí)驗(yàn)結(jié)果： 實(shí)驗(yàn)七 三．已知下列傳遞函數(shù)H(s)或H(z)，求其極零點(diǎn)，并畫(huà)出極零圖。 1. >> z=[1,2]'; p=[-1,-2]'; zplane(z,p) 實(shí)驗(yàn)結(jié)果： 2. >> z=[1,2]; p=[-1,-2]; zplane(z,p) >> num=[1]; den=[1,0]; [z,p,k]=tf2zp(num,den); zplane(z,p) >> num=[1]; den=[1,0]; [z,p,k]=tf2zp(num,den) zplane(z,p) 實(shí)驗(yàn)結(jié)果： z = Empty matrix: 0-by-1 p = 0 k = 1 3. >> num=[1,0,1]; den=[1,2,5]; [z,p,k]=tf2zp(num,den) zplane(z,p) 實(shí)驗(yàn)結(jié)果： z = 0 + 1.0000i 0 - 1.0000i p = -1.0000 + 2.0000i -1.0000 - 2.0000i k = 1 4. >> num=[1.8,1.2,1.2,3]; den=[1,3,2,1]; [z,p,k]=tf2zp(num,den) zplane(z,p) 實(shí)驗(yàn)結(jié)果： z = -1.2284 0.2809 + 1.1304i 0.2809 - 1.1304i p = -2.3247 -0.3376 + 0.5623i -0.3376 - 0.5623i k = 1.8000 5． >> clear; A=[0,1,0; 0,0,1; -6,-11,-6]; B=[0;0;1]; C=[4,5,1]; D=0; sys5=ss(A,B,C,D); pzmap(sys5) 實(shí)驗(yàn)結(jié)果： 五．求出下列系統(tǒng)的極零點(diǎn)，判斷系統(tǒng)的穩(wěn)定性。 1. >> clear; A=[5,2,1,0; 0,4,6,0; 0,-3,-6,-1;1,-2,-1,3]; B=[1;2;3;4]; C=[1,2,5,2]; D=0; sys=ss(A,B,C,D); [z,p,k]=ss2zp(A,B,C,D,1) pzmap(sys) 實(shí)驗(yàn)結(jié)果： z = 4.0280 + 1.2231i 4.0280 - 1.2231i 0.2298 p = -3.4949 4.4438 + 0.1975i 4.4438 - 0.1975i 0.6074 k = 28 由求得的極點(diǎn)，該系統(tǒng)不穩(wěn)定。 4. >>z=[-3] P=[-1,-5,-15] 所以該系統(tǒng)為穩(wěn)定的。 5. >>num=100*conv([1,0],conv([1,2],conv([1,2],conv([1,3,2],[1,3,2])))); den=conv([1,1],conv([1,-1],conv([1,3,5,2],conv([1,0,2,0,4],[1,0,2,0,4])))); [z,p,k]=tf2zp(num,den) 實(shí)驗(yàn)結(jié)果： z = 0 -2.0005 + 0.0005i -2.0005 - 0.0005i -1.9995 + 0.0005i -1.9995 - 0.0005i -1.0000 + 0.0000i -1.0000 - 0.0000i p = 1.0000 0.7071 + 1.2247i 0.7071 - 1.2247i 0.7071 + 1.2247i 0.7071 - 1.2247i -1.2267 + 1.4677i -1.2267 - 1.4677i -0.7071 + 1.2247i -0.7071 - 1.2247i -0.7071 + 1.2247i -0.7071 - 1.2247i -1.0000 -0.5466 >>zplane(z,p) 所以該系統(tǒng)不穩(wěn)定。 七．已知反饋系統(tǒng)開(kāi)環(huán)轉(zhuǎn)移函數(shù)如下，試作其奈奎斯特圖，并判斷系統(tǒng)是否穩(wěn)定。 1. >> b=[1]; a=[1,3,2]; sys=tf(b,a); nyquist(sys); 實(shí)驗(yàn)結(jié)果： 由于奈奎斯特圖并未圍繞上-1點(diǎn)運(yùn)動(dòng)，同時(shí)其開(kāi)環(huán)轉(zhuǎn)移函數(shù)也是穩(wěn)定的，由此，該線性負(fù)反饋系統(tǒng)也是穩(wěn)定的。 2． >> b=[1]; a=[1,4,4,0]; sys=tf(b,a); nyquist(sys); 實(shí)驗(yàn)結(jié)果： 由于奈奎斯特圖并未圍繞上-1點(diǎn)運(yùn)動(dòng)，同時(shí)其開(kāi)環(huán)轉(zhuǎn)移函數(shù)也是穩(wěn)定的，由此，該線性負(fù)反饋系統(tǒng)也是穩(wěn)定的。 3. >> b=[1]; a=[1,2,2]; sys=tf(b,a); nyquist(sys); 實(shí)驗(yàn)結(jié)果： 由于奈奎斯特圖并未圍繞上-1點(diǎn)運(yùn)動(dòng)，同時(shí)其開(kāi)環(huán)轉(zhuǎn)移函數(shù)也是穩(wěn)定的，由此，該線性負(fù)反饋系統(tǒng)也是穩(wěn)定的。 練習(xí)三 實(shí)驗(yàn)三 五． 1． >>help window WINDOW Window function gateway. WINDOW(@WNAME,N) returns an N-point window of type specified by the function handle @WNAME in a column vector. @WNAME can be any valid window function name, for example: @bartlett - Bartlett window. @barthannwin - Modified Bartlett-Hanning window. @blackman - Blackman window. @blackmanharris - Minimum 4-term Blackman-Harris window. @bohmanwin - Bohman window. @chebwin - Chebyshev window. @flattopwin - Flat Top window. @gausswin - Gaussian window. @hamming - Hamming window. @hann - Hann window. @kaiser - Kaiser window. @nuttallwin - Nuttall defined minimum 4-term Blackman-Harris window. @parzenwin - Parzen (de la Valle-Poussin) window. @rectwin - Rectangular window. @tukeywin - Tukey window. @triang - Triangular window. WINDOW(@WNAME,N,OPT) designs the window with the optional input argument specified in OPT. To see what the optional input arguments are, see the help for the individual windows, for example, KAISER or CHEBWIN. WINDOW launches the Window Design & Analysis Tool (WinTool). EXAMPLE: N = 65; w = window(@blackmanharris,N); w1 = window(@hamming,N); w2 = window(@gausswin,N,2.5); plot(1:N,[w,w1,w2]); axis([1 N 0 1]); legend('Blackman-Harris','Hamming','Gaussian'); See also bartlett, barthannwin, blackman, blackmanharris, bohmanwin, chebwin, gausswin, hamming, hann, kaiser, nuttallwin, parzenwin, rectwin, triang, tukeywin, wintool. Overloaded functions or methods (ones with the same name in other directories) help fdesign/window.m Reference page in Help browser doc window 2. >>N = 128; w = window(@rectwin,N); w1 = window(@bartlett,N); w2 = window(@hamming,N); plot(1:N,[w,w1,w2]); axis([1 N 0 1]); legend('矩形窗','Bartlett','Hamming'); 3. >>wvtool(w,w1,w2) 六． ts=0.01; N=20; t=0:ts:(N-1)*ts; x=2*sin(4*pi*t)+5*cos(6*pi*t); g=fft(x,N); y=abs(g)/100; figure(1):plot(0:2*pi/N:2*pi*(N-1)/N,y); grid; ts=0.01; N=30; t=0:ts:(N-1)*ts; x=2*sin(4*pi*t)+5*cos(6*pi*t); g=fft(x,N); y=abs(g)/100; figure(2):plot(0:2*pi/N:2*pi*(N-1)/N,y); grid; ts=0.01; N=50; t=0:ts:(N-1)*ts; x=2*sin(4*pi*t)+5*cos(6*pi*t); g=fft(x,N); y=abs(g)/100; figure(3):plot(0:2*pi/N:2*pi*(N-1)/N,y); grid; ts=0.01; N=100; t=0:ts:(N-1)*ts; x=2*sin(4*pi*t)+5*cos(6*pi*t); g=fft(x,N); y=abs(g)/100; figure(4):plot(0:2*pi/N:2*pi*(N-1)/N,y); grid; ts=0.01; N=150; t=0:ts:(N-1)*ts; x=2*sin(4*pi*t)+5*cos(6*pi*t); g=fft(x,N); y=abs(g)/100; figure(5):plot(0:2*pi/N:2*pi*(N-1)/N,y); grid; 實(shí)驗(yàn)八 1． %沖激響應(yīng) >> clear; b=[1,3]; a=[1,3,2]; sys=tf(b,a); impulse(sys); 結(jié)果： %求零輸入響應(yīng) >> A=[1,3;0,-2]; B=[1;2]; Q=A\B Q = 4 -1 >> clear B=[1,3]; A=[1,3,2]; [a,b,c,d]=tf2ss(B,A) sys=ss(a,b,c,d); x0=[4;-1]; initial(sys,x0); grid; a = -3 -2 1 0 b = 1 0 c = 1 3 d = 0 2. %沖激響應(yīng) >> clear; b=[1,3]; a=[1,2,2]; sys=tf(b,a); impulse(sys) %求零輸入響應(yīng) >> A=[1,3;1,-2]; B=[1;2]; Q=A\B Q = 1.6000 -0.2000 >> clear B=[1,3]; A=[1,2,2]; [a,b,c,d]=tf2ss(B,A) sys=ss(a,b,c,d); x0=[1.6;-0.2]; initial(sys,x0); grid; a = -2 -2 1 0 b = 1 0 c = 1 3 d = 0 3. %沖激響應(yīng) >> clear; b=[1,3]; a=[1,2,1]; sys=tf(b,a); impulse(sys) %求零輸入響應(yīng) >> A=[1,3;1,-1]; B=[1;2]; Q=A\B Q = 1.7500 -0.2500 >> clear B=[1,3]; A=[1,2,1]; [a,b,c,d]=tf2ss(B,A) sys=ss(a,b,c,d); x0=[1.75;-0.25]; initial(sys,x0); grid; a = -2 -1 1 0 b = 1 0 c = 1 3 d = 0 二． >> clear; b=1; a=[1,1,1,0]; sys=tf(b,a); subplot(2,1,1); impulse(sys);title('沖擊響應(yīng)'); subplot(2,1,2); step(sys);title('階躍響應(yīng)'); t=0:0.01:20; e=sin(t); r=lsim(sys,e,t); figure; subplot(2,1,1); plot(t,e);xlabel('Time');ylabel('A');title('激勵(lì)信號(hào)'); subplot(2,1,2); plot(t,r);xlabel('Time');ylabel('A');title('響應(yīng)信號(hào)'); 三． 1. >> clear; b=[1,3]; a=[1,3,2]; t=0:0.08:8; e=[exp(-3*t)]; sys=tf(b,a); lsim(sys,e,t); 2. >> clear; b=[1,3]; a=[1,2,2]; t=0:0.08:8; sys=tf(b,a); step(sys) 3． >> clear; b=[1,3]; a=[1,2,1]; t=0:0.08:8; e=[exp(-2*t)]; sys=tf(b,a); lsim(sys,e,t); Doc: 1. >> clear; B=[1]; A=[1,1,1]; sys=tf(B,A,-1); n=0:200; e=5+cos(0.2*pi*n)+2*sin(0.7*pi*n); r=lsim(sys,e); stem(n,r); 2. >> clear; B=[1,1,1]; A=[1,-0.5,-0.5]; sys=tf(B,A,-1); e=[1,zeros(1,100)]; n=0:100; r=lsim(sys,e); stem(n,r); 練習(xí)三 實(shí)驗(yàn)三 五． 1． >>help window WINDOW Window function gateway. WINDOW(@WNAME,N) returns an N-point window of type specified by the function handle @WNAME in a column vector. @WNAME can be any valid window function name, for example: @bartlett - Bartlett window. @barthannwin - Modified Bartlett-Hanning window. @blackman - Blackman window. @blackmanharris - Minimum 4-term Blackman-Harris window. @bohmanwin - Bohman window. @chebwin - Chebyshev window. @flattopwin - Flat Top window. @gausswin - Gaussian window. @hamming - Hamming window. @hann - Hann window. @kaiser - Kaiser window. @nuttallwin - Nuttall defined minimum 4-term Blackman-Harris window. @parzenwin - Parzen (de la Valle-Poussin) window. @rectwin - Rectangular window. @tukeywin - Tukey window. @triang - Triangular window. WINDOW(@WNAME,N,OPT) designs the window with the optional input argument specified in OPT. To see what the optional input arguments are, see the help for the individual windows, for example, KAISER or CHEBWIN. WINDOW launches the Window Design & Analysis Tool (WinTool). EXAMPLE: N = 65; w = window(@blackmanharris,N); w1 = window(@hamming,N); w2 = window(@gausswin,N,2.5); plot(1:N,[w,w1,w2]); axis([1 N 0 1]); legend('Blackman-Harris','Hamming','Gaussian'); See also bartlett, barthannwin, blackman, blackmanharris, bohmanwin, chebwin, gausswin, hamming, hann, kaiser, nuttallwin, parzenwin, rectwin, triang, tukeywin, wintool. Overloaded functions or methods (ones with the same name in other directories) help fdesign/window.m Reference page in Help browser doc window 2. >>N = 128; w = window(@rectwin,N); w1 = window(@bartlett,N); w2 = window(@hamming,N); plot(1:N,[w,w1,w2]); axis([1 N 0 1]); legend('矩形窗','Bartlett','Hamming'); 3. >>wvtool(w,w1,w2) 六． ts=0.01; N=20; t=0:ts:(N-1)*ts; x=2*sin(4*pi*t)+5*cos(6*pi*t); g=fft(x,N); y=abs(g)/100; figure(1):plot(0:2*pi/N:2*pi*(N-1)/N,y); grid; ts=0.01; N=30; t=0:ts:(N-1)*ts; x=2*sin(4*pi*t)+5*cos(6*pi*t); g=fft(x,N); y=abs(g)/100; figure(2):plot(0:2*pi/N:2*pi*(N-1)/N,y); grid; ts=0.01; N=50; t=0:ts:(N-1)*ts; x=2*sin(4*pi*t)+5*cos(6*pi*t); g=fft(x,N); y=abs(g)/100; figure(3):plot(0:2*pi/N:2*pi*(N-1)/N,y); grid; ts=0.01; N=100; t=0:ts:(N-1)*ts; x=2*sin(4*pi*t)+5*cos(6*pi*t); g=fft(x,N); y=abs(g)/100; figure(4):plot(0:2*pi/N:2*pi*(N-1)/N,y); grid; ts=0.01; N=150; t=0:ts:(N-1)*ts; x=2*sin(4*pi*t)+5*cos(6*pi*t); g=fft(x,N); y=abs(g)/100; figure(5):plot(0:2*pi/N:2*pi*(N-1)/N,y); grid; 實(shí)驗(yàn)八 1． %沖激響應(yīng) >> clear; b=[1,3]; a=[1,3,2]; sys=tf(b,a); impulse(sys); 結(jié)果： %求零輸入響應(yīng) >> A=[1,3;0,-2]; B=[1;2]; Q=A\B Q = 4 -1 >> clear B=[1,3]; A=[1,3,2]; [a,b,c,d]=tf2ss(B,A) sys=ss(a,b,c,d); x0=[4;-1]; initial(sys,x0); grid; a = -3 -2 1 0 b = 1 0 c = 1 3 d = 0 2. %沖激響應(yīng) >> clear; b=[1,3]; a=[1,2,2]; sys=tf(b,a); impulse(sys) %求零輸入響應(yīng) >> A=[1,3;1,-2]; B=[1;2]; Q=A\B Q = 1.6000 -0.2000 >> clear B=[1,3]; A=[1,2,2]; [a,b,c,d]=tf2ss(B,A) sys=ss(a,b,c,d); x0=[1.6;-0.2]; initial(sys,x0); grid; a = -2 -2 1 0 b = 1 0 c = 1 3 d = 0 3. %沖激響應(yīng) >> clear; b=[1,3]; a=[1,2,1]; sys=tf(b,a); impulse(sys) %求零輸入響應(yīng) >> A=[1,3;1,-1]; B=[1;2]; Q=A\B Q = 1.7500 -0.2500 >> clear B=[1,3]; A=[1,2,1]; [a,b,c,d]=tf2ss(B,A) sys=ss(a,b,c,d); x0=[1.75;-0.25]; initial(sys,x0); grid; a = -2 -1 1 0 b = 1 0 c = 1 3 d = 0 二． >> clear; b=1; a=[1,1,1,0]; sys=tf(b,a); subplot(2,1,1); impulse(sys);title('沖擊響應(yīng)'); subplot(2,1,2); step(sys);title('階躍響應(yīng)'); t=0:0.01:20; e=sin(t); r=lsim(sys,e,t); figure; subplot(2,1,1); plot(t,e);xlabel('Time');ylabel('A');title('激勵(lì)信號(hào)'); subplot(2,1,2); plot(t,r);xlabel('Time');ylabel('A');title('響應(yīng)信號(hào)'); 三． 1. >> clear; b=[1,3]; a=[1,3,2]; t=0:0.08:8; e=[exp(-3*t)]; sys=tf(b,a); lsim(sys,e,t); 2. >> clear; b=[1,3]; a=[1,2,2]; t=0:0.08:8; sys=tf(b,a); step(sys) 3． >> clear; b=[1,3]; a=[1,2,1]; t=0:0.08:8; e=[exp(-2*t)]; sys=tf(b,a); lsim(sys,e,t); Doc: 1