实验4离散系统的分析

实验四离散系统分析深刻理解离散时间系统的系统函数在分析离散系统的时域特性、频域特性以LA特性和零极点的方法。掌握利用DTFT和DFT确定系统特性的原理和方法。可以在时域、复频域(Z域)及频域分析系统，在以上三种域表征系统固有特性的量分单位冲激响应h(n)(时域表征)；系统函数H(z)(Z域表征)；频率响应H(ep)(频域表征)。MATLA吐要从以上三方面提供了许多可用于分析线性时不变系统的函数，包含系统时域响应、系统函数、系统频域响应等分析函数。本实验通过调用各种系统预置函数来求系统的以上几个表征量以及零极点图。y[k]-1.143y[k-1]0.412y[k-2]=0.0675x[k]0.1349x[k-1]0.0675x(^2]b1349,0.0675];a3,0.412];xones(1,N);zifilticba2]);yfilterba,x,zi);xlabelk;title('y[k]');结果:y[k]二二7二xdk]=cos(k)u[k];X2【k]=cosUk)u[k];X3[k]=cos(k)u[k]10510程序N0;k=O:N;b1394,0.0675];a3,0.412];x1=cos(pi*0.1.*k);x2=cos(pi*0.2*k);x3=cos(pi*0.7*k);yfilter(b,a,x1);yfilter(b,a,x2);yfilter(b,a,x3);ubplotubplot(3)该系统具有什么特性?答：因果稳定。(1)计算系统的单位冲激响应b=[0.0357,0.1428,0.2143,0.1428,0.0357];a=[1,-1.035,0.8264,-0.2605,0.04033];yimpz(b,a,N);(2)当信号x[kHu[k]cos(^k)u[k]cos(2k)u[k]通过系统时，计算系统的零状态响应。b357,0.1428,0.2143,0.1428,0.0357];a1,-1.035,0.8264,-0.2605,0.04033];x=ones(1,N)+cos(pi*0.25*k)+cos(0.5*pi*k);yimpz(b,a,N);yfilterb,a,x);ubplotubplotO.B04051Q1520253D40455D(a)x[k]=(*)ku[k],y[k]=*(1)ku[k]讨)ku[k](b)x[k]=(》ku[k],y[k]=(4)ku[k]-(-l)klu[k-1]已知LTI系统的输入输出序列分别为x[k]aNsubplot1,1);hb-1];aNsubplot1,2);ha6I(2)利用系统辨识原理确定并求出系统的单位脉冲响应h[k]。比较解析方法与系统辨识方法得到的系统单位冲激响应，分析误差原因。x1=0.5.Ak;y1=0.25*0.5.Ak+0.25.Ak;X1=fft(x1);X2=0.25.An;y2=0.25.An-4*0.254n;X=fft(x2);Y2=fft(y2);hi二H(ej)误差原因：取样点数不够多引起的误差，而且不易与k对应4.已知某离散系统的输入输出序列。，序-0.4974,0.7711,-1.1267,1.5702,-2.1037,2.724,-3.4207,4.174,-4.9528，5.7117,-6.3889,6.9034,-7.1528,7.012,-6.3322,4.9416,-2.648,-0.7564,5.4872,-11.7557,19.7533,-29.6298,41.4666,-55.2433,70.7979,-x0.3611,0.162,0.0748,0.0354,0.017,0.0083,0.0041,0.002,0001,0.0001,zeros(1,16)];y0.0259,0.073,-0.1593,0.297,-0.4974,0.7711,-1.1267,.4207,4.174,-4.9528,5.7117,-6.3889,6.9034,-7.1528,7.012,-6.3322,4.9416,-2.648,-0.7564,5.4872,-11.7557,19.7533,-666,-55.2433,70.7979,-87.7810];tt结果：ia0|-ia0|-SO-f■50--1Dol--------------------1-----------------1-----------------1-----------------1-------------------1-------------------1-^-----------------10510te20茁303G(2)计算该系统的频率响应，并绘出其幅频特性。x.162,0.0748,0.0354,0.017,0.0083,0.0041,0.002,.0001,zeros(1,16)];y.073,-0.1593,0.297,-0.4974,0.7711,-1.1267,8,5.7117,-6.3889,6.9034,322,4.9416,-2.648,-0.7564,5.4872,-11.7557,19.7533,-29.6298,41.4666,-55.2433,70.7979,-87.7810];Xfftx,128);Y=fft(y,128);3)计算该系统的单位冲激响应，并绘出其波形。x,0.3611,0.162,0.0748,0.0354,0.017,0.0083,0.0041,0.002,0001,0.0001,zeros(1,16)];y-0.0259,0.073,-0.1593,0.297,-0.4974,0.7711,-1.1267,.4207,4.174,-4.9528,5.7117,-6.3889,6.9034,-7.1528,7.012,-6.3322,4.9416,-2.648,-0.7564,5.4872,-11.7557,19.7533,-666,-55.2433,70.7979,-87.7810];ftxYffty);h-E2bL.7687辺COInJnIS+COIUJILTLS56++图形为:利用loadmtlb命令读入一段语音信号得到序列,然后在该段语音信号HzFFT (1)下列数字滤波器能够滤除信号中500Hz正弦型干扰信号。0.6877-2.509z"3.664z_2-2.509z"H(z)0.6877z"二 1-3.594z_15.172z_2-3.494z_30.945z"利用zplane命令做出其零极点分布图，利用freqz命令分析该滤波器的幅频特性和相频特性，比较零极点分布与滤波器频率特性的关系。a4,0.945];b9,0.6877];title('零极点分布')[H,w]=freqz(b,a);subplot(2,2,2);plot(w,abs(H))xlabel('\omega(rad)');ylabel('HO');title('幅频特性');subplot(2,2,3);plot(w,angle(H))xlabel('\omega(rad)');ylabel('\phi');title('相频特性');结果：505Q->n匸一rE.存M006TM006To6关系：系统零点越接近1贝肿畐频响应的波谷越低，即滤波器的滤波衰减最低点越低；系统极点越接近1贝肿畐频响应的波峰越高，即滤波器的滤波通带最高点越高。极点主要影响频率响应的峰值，极点愈靠近单位圆，峰值愈尖锐；零点主要影响频率特性的谷值，零点愈靠近单位圆，谷值愈深，当零点在单位圆上时，频率特性为零，一个传递函数(2)利用该数字滤波器滤除信号中的噪声，利用函数播放处理前后的信号，比较处理前后的效果。程序；tlbNplot(k,x);title('处理前');X=fft(x,150);h=ifft(H);H=fft(H,150);Y=X.*H;y=ifft(Y);实验思考题ANS系统零点越接近1,贝肿畐频响应的波谷越低，即滤波器的滤波衰减最低点越低；系统极点越接近1,贝肿畐频响应的波峰越高，即滤波器的滤波通带最高点越高。极点主要影响频率响应的峰值，极点愈靠近单位圆，峰值愈尖锐；零点主要影响频率特性的谷值，零点愈靠近单位圆，谷值愈深，当零点在单位圆上时，频率特性为零，一个传递函谷值。2.对于因果稳定实系数的低通、高通、带通、带阻数字滤波器，零极点分布有何特点？ANS:因为是因果稳定系统，所以极点都在单位圆内。若为最小相位系统，其零点也3.离散系统的系统函数的零极点对系统脉冲响应有何影响？ANS系统函数的极点位置决定序列包络的变化趋势和变化频率，极点的半径决定了序列包络的变化趋势，而极点的幅角决定序列包络的变化频率，而零点位