文档介绍：信号与系统基本概念h(k)h(t)f(t) y(t) f(k) y(k)常用信号ε(t) δ(t) cos(ωt+Ф)est ε(k) δ(k) cos(ωk+Ф)akesk 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)/dt x(k)=x1(k)-x1(k-1)ex1:y(t)=(t+2)*(ε(t+2)-ε(t))+2ε(t)-2ε(t-2)y(1-2t)=?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(π/3k)+cos(π/4k) 周期信号? f(k):N=2π/2=π g(k):N=m1*N1=m2*N2 N1=2π/(π/3)=6 N2=8; N=m1*6=8*m2 N=m1*3=4*m2 m1=4m2=3 N=4*6=24;奇偶函数x(-t)=x(t)x(-t)=-x(t)系统分类LTI----线性时不变系统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)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(ωCt) 线性?时不变?Ifx(t)=a1*x1(t)+a2*x2(t) Theny(t)=(a1*x1(t)+a2*x2(t))*cos(ωCt) =a1*x1(t)*cos(ωCt)+a2*x2(t)*cos(ωCt) =a1*y1(t)+a2*y2(t) 线性 ifx(t)=x1(t-t0) y(t)=x(t)*cos(ωCt) =x1(t-t0)*cos(ωCt) y1(t-t0)=x1(t-t0)*cos(ωCt-ωCt0) y(t)!=y1(t-t0) 时变 1) y(t)=f(x(t)) y(t)仅与现在和过去的x值有关(x(t-τ)τ>=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) LTI h(t)=0t<0 h(k)=0k<0 3) LTI H(s)ROC:Right-halfplane H(z)ROC:ExteriorofaCircle(+∞) H(s) rational ROC:Right-otherightm