信号与系统
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f(2t)f(2-2t)第二章 单位跃阶 k=-50:50;uk=[zeros(1,50),ones(1,51)]; stem(k,uk)信号的尺度变换、翻转、平移 >> t=-3:0.001:3;>> ft1=tripuls(2*t,4,0.5); >> subplot(2,1,1) >> plot(t,ft1) >> title('f(2t)')>> ft2=tripuls((2-2*t),4,0.5); >> subplot(2,1,2) >> plot(t,ft2) >> title('f(2-2t)')指数信号>> A=1;a=-0.4; >> t=0:0.01:10; >> ft=A*exp(a*t); >> plot(t,ft)抽样函数>> t=-3*pi:pi/100:3*pi; >> ft=sinc(t/pi); >> plot(t,ft)单位脉冲 >> t=-50:50;delta=[zeros(1,50),1,zeros(1,50)]; >> stem(t,delta)Time(sec)y (t )Time(sec)y (t )MATLAB 习题2-1（3） >> A=10;a=-1;B=-5;b=-2; >> t=0:0.01:5;>> ft=A*exp(a*t)+B*exp(b*t); >> plot(t,ft)指数序列>> k=0:10;A=1;a=-0.6; >> fk=A*a.^k; >>stem(k,fk)第三章连续时间系统零状态响应ts=0;te=5;dt=0.01; sys=tf([1],[1 2 100]); t=ts:dt:te;f=10*sin(2*pi*t); y=lsim(sys,f,t); plot(t,y);xlabel('Time(sec)') ylabel('y(t)')连续时间系统冲激响应和阶跃响应 >> ts=0;te=5;dt=0.01; >> sys=tf([10],[1 2 100]); >> t=ts:dt:te;>> y=impulse(sys,t);>> plot(t,y); >> xlabel('Time(sec)') >> ylabel('y(t)')Cn 的幅度ω/ωCn 的相位ω/ω0离散卷积计算 [例3-38]>> A=4;a=-0.5; >> t=0:10; >> w0=pi;>> ft=A*exp(a*t)*cos(w0*t);习题3-16（6）t=0:0.1:10; x=2*exp(-2*t); y=0;z=conv(x,y); N=length(z); plot(0:N-1,z);习题3-16（7）t=0:-0.1:-10; x=2*exp(2*t); y=3*exp(t); z=conv(x,y); N=length(z); plot(0:N-1,z);第四章例4-11三角波信号的频谱N=8; n1=-N:-1;c1=-4*j*sin(n1*pi/2)/pi^2./n1.^2; c0=0; n2=1:N;c2=-4*j*sin(n2*pi/2)/pi^2./n2.^2; cn=[c1 c0 c2]; n=-N:N;subplot(1,2,1); stem(n,abs(cn));ylabel('Cn 的幅度');xlabel('\omega/\omega0');-20-15-10-505101520F (j ω)-9ω计算误差subplot(1,2,2); stem(n,angle(cn)); ylabel('Cn 的相位');xlabel('\omega/\omega0');例４-１２t=-2:0.001:2; N=input('N='); c0=0.5;fN=c0*ones(1,length(t)); for n=1:2:NfN=fN+cos(pi*n*t)*sinc(n/2); endplot(t,fN);title('N='，num2str(N)); axis([-2 2 -0.2 1.2]);第五章例5-19function y=sf1(t,w);y=(t>=-1&t<=1).*(1-abs(t)).*exp(-j*w*t);w=linspace(-6*pi,6*pi,512); N=length(w);F=zeros(1,N); for k=1:NF(k)=quad8('sf1',-1,1,[],[],w(k)); end figure(1); plot(w,real(F)); xlabel('\omega'); ylabel('F(j\omega)'); figure(2);plot(w,real(F)-sinc(w/2/pi).^2); xlabel('\omega'); title('计算误差');例 5-200.20.40.60.81 1.2 1.4 1.6 1.82HzE012345ω|H (j ω)|12345ωφ(ω)function y=sf2(t) y=2*sinc(t).*sinc(t);f=linspace(0,5,256); N=length(f);w=zeros(1,N); for k=1:Nw(k)=quad8('sf2',0,f(k)); end plot(f,w); xlabel('Hz'); ylabel('E');例5-21b=[1];a1=[1 -0.9];a2=[1 0.9]; w=linspace(0,2*pi,512); h1=freqz(b,a1,w); h2=freqz(b,a2,w);plot(w/pi,abs(h1),w/pi,abs(h2),':'); legend('\alpha=0.9','\alpha=-0.9');第六章P206 例6-16w=linspace(0,5,200); b=[1]; a=[1 2 2 1]; H=freqs(b,a,w);subplot(2,1,1); plot(w,abs(H));set(gca,'xtick',[0 1 2 3 4 5]); set(gca,'ytick',[0 0.4 0.707 1]); grid;xlabel('\omega'); ylabel('|H(j\omega)|');subplot(2,1,2); plot(w,angle(H));set(gca,'xtick',[0 1 2 3 4 5]); grid;xlabel('\omega'); ylabel('\phi(\omega)');Time(s)y (t )P208 习题6-1t=linspace(0,5,1000); w=3;H=j*4*w/((j*w)^2+j*6*w+8); f=cos(3*t);y=abs(H)*cos(w*t+angle(H)); plot(t,y);xlabel('Time(s)'); ylabel('y(t)');第七章 M7-1 （1）num=[0 41.6667];den=[1 3.7444 25.7604 41.6667]; [r,p]=residue(num,den) r =-0.9361 - 0.1895i -0.9361 + 0.1895i 1.8722 p =-0.9361 + 4.6237i -0.9361 - 4.6237i -1.8722 F （s ）=（-0.9361 - 0.1895i ）/((-0.9361 + 4.6237i)+ s)+( -0.9361 + 0.1895i)/(( -0.9361 - 4.6237i)+s)^2+1.8722/(-1.8722+s)^3 M7-3 (1)num=[1];den=[1 2*(sin(pi/8)+sin(3*pi/8)) 2+4*sin(pi/8)*sin(3*pi/8) 2*(sin(pi/8)+sin(3*pi/8)) 1]; [r,p]=residue(num,den)Real AxisI m a g i n a r y A x i sr =-0.4619 + 0.1913i -0.4619 - 0.1913i 0.4619 - 1.1152i 0.4619 + 1.1152i p =-0.3827 + 0.9239i -0.3827 - 0.9239i -0.9239 + 0.3827i -0.9239 - 0.3827i例7-31 num=[1];den=[1 2 2 1]; sys=tf(num,den); poles=roots(den); figure(1);pzmap(sys); t=0:0.02:10;h=impulse(num,den,t); figure(2);plot(t,h)title('Impulse Respone') [H,w]=freqs(num,den); figure(3);plot(w,abs(H)) xlabel('\omega')title('Magnitude Respone')m a g n a r y A x s0.050.10.150.2Time(s)Modulate SignalFrequency(Hz)Modulate Signal0.050.10.150.2Time(s)Modulate Signal(AM)Frequency(Hz)Modulate Signal(AM)M7-5num=[1 2]; den=[1 2 2 1]; sys=tf(num,den); poles=roots(den); figure(1);pzmap(sys); t=0:0.02:10;h=impulse(num,den,t); figure(2);plot(t,h)title('Impulse Respone') [H,w]=freqs(num,den); figure(3);plot(w,abs(H)) xlabel('\omega')title('Magnitude Respone')调制正弦信号前后P374 调制正弦信号前后Fm=10;Fc=100;Fs=1000;N=1000; k=0:N-1; t=k/Fs;x=sin(2.0*pi*Fm*t); subplot(2,2,1);plot(t(1:200),x(1:200)); axis([0,0.2,-1,1]); xlabel('Time(s)'); title('Modulate Signal'); Xf=abs(fft(x,N)); subplot(2,2,2); stem(Xf(1:200)); xlabel('Frequency(Hz)'); title('Modulate Signal'); y=modulate(x,Fc,Fs,'am'); subplot(2,2,3);plot(t(1:200),y(1:200)); axis([0,0.2,-1,1]); xlabel('Time(s)');title('Modulate Signal(AM)'); Xf=abs(fft(y,N)); subplot(2,2,4); stem(Xf(1:200)); xlabel('Frequency(Hz)'); title('Modulate Signal(AM)');nTsf (n T s )抽样信号Ts=0.02时的抽样信号f(nTs)抽样wm=40*pi;wc=1.2*wm; Ts=[0.02 0.03]; N=length(Ts)；n=-100:100; nTs=n*Ts(k);fs=(cos(8*pi*nTs)+2*sin(40*pi*nTs)+cos(24*pi*nTs)).*((nTs+pi)-(nTs-pi ));t=-0.25:0.001:0.25;ft=fs*Ts(k)*wc/pi*sinc((wc/pi)*(ones(length(nTs),1)*t-nTs'*ones(1,len gth(t))));t1=-0.25:0.001:0.25;f1=(cos(8*pi*t1)+2*sin(40*pi*t1)+cos(24*pi*t1)).*((t1+0.25)-(t1-0.25));%在一副图中画原连续信号f(t)和样信号f_s(t)。
