信号与系统基本概念.doc

信号与系统基本概念h(k)h(t)f(t)y(t)f(k)y(k)一. 常用信号(t)(t)cos(t+) est(k)(k)cos(k+) ak esk二. 信号常用运算x(t)=x1(t)+x2(t)x(k)=x1(k)+x2(k)x(t)=x1(t)-x2(t)x(k)=x1(k)-x2(k)x(t)=x1(-t)x(k)=x1(-k)x(t)=x1(t-t0)x(k)=x1(k-k0)x(t)=x1(at)x(k)=x1(ak)x(t)=x1(at-t0)x(k)=x1(ak-k0)x(t)=dx1(t)/dtx(k)=x1(k)-x1(k-1)ex1:y(t)=(t+2)*(t+2)-(t) +2(t)-2(t-2)y(1-2t)=?三. 周期信号与非周期信号f(t+T)=f(t)f(n+N)=f(n)ex2:f(k)=cos(2k)g(k)=cos(/3k)+cos(/4k)周期信号?f(k): N=2/2= g(k): N=m1*N1=m2*N2 N1=2/(/3)=6N2=8;N=m1*6=8*m2N=m1*3=4*m2m1=4 m2=3N=4*6=24;四. 奇偶函数x(-t)=x(t)x(-t)=-x(t)五. 系统分类LTI-线性时不变系统1. 线性与非线性系统线性:零状态下:a1*x1(t)+a2*x2(t) a1*y1(t)+a2*y2(t)a1*x1(k)+a2*x2(k) a1*y1(k)+a2*y2(k)2. 时不变与时变系统时不变x(t-t0) y(t-t0)x(k-k0) y(k-k0)ex3:y(t)=x(t)*cos (Ct)线性? 时不变?If x(t)= a1*x1(t)+a2*x2(t)Then y(t)=(a1*x1(t)+a2*x2(t) *cos (Ct)= a1*x1(t) *cos (Ct)+ a2*x2(t)* cos (Ct)=a1*y1(t)+a2*y2(t)线性if x(t)=x1(t-t0)y(t)=x(t)*cos (Ct)= x1(t-t0) *cos (Ct)y1(t-t0)=x1(t-t0)*cos (Ct-Ct0)y(t)!= y1(t-t0)时变3.因果与非因果系统1)y(t)=f(x(t)y(t) 仅与现在和过去的x值有关(x(t-) =0)y(k)=f(x(k)y(k) 仅与现在和过去的x值有关(x(k-n) n=0)2)LTIh(t)=0 t0h(k)=0 k0 3)LTI H(s) ROC: Right-half planeH(z) ROC: Exterior of a Circle (+)H(s) rationalROC: Right-half plane to the rightmost poleH(z) rationalROC: Exterior of a Circle outside the rightmost polethe order of numerator1/23. 稳定与非稳定系统1)BIBOx(t) 有界y(t) 有界x(k)有界y(k) 有界 2）LTI-+|h()|/d+k=-+|h(k)|+3)LTIH(s)ROC Include jw axisH(Z) ROC Include |z|=1Rational & CausalH(s)Poles lie in left-half