University:
College
Course:
College Mathematics
Academic year:

2023
Views:

5

Pages:

1
Author:

anon

Table of Laplace and Z-transformsX(s)x(t)x(kT) or x(k)X(z)Kronecker delta So(k)1.--1k=010k # 0So(n-k)2.--1 n=kz-K0n k k113.-1(t)1(k)S1-z-114.e-ate-akTs+a1-e-drTz-15.s2tkT(1 - z-1)226.t(kT)2S3(1-z-1)67.t3(kT)3s4(1-z-1)a8.1-e-at1 - e-akT(1-e-a)s(s+a)b-a9.e-at - e-br(e-aT -e-bT)(s+a)(s+b)110.te-atkTe-akT(s+a)2(1-e-d'z-1)2S1-(1+aT)e-T11.(s+a)2(1-at)e-an(1 - akT)e-akT212.te-at(s+a)(kT)2e-akT(1-e-d'z-1)3a213.at - 1 +akT - 1 + Ts2(s+a)zis aT14.s2+w2sin atsin akT1-2z-1 cos aT + z11-z-1 cos aT15.cos atcos akT1-2z-cos oT+za16.(s+a)2+w2e-arte-akT sin wkT1-2e-acoswTe2aT2s+a17.e-arte-akT cos akT(s+a)2 +w22e-aT-cos wT+e-2aT18.--ak1-az-1akz-119.--k=1,2,3,1-az-12-120.--kak-1(1-az-1)221.--kak-1(1-az-1)22.--k3a--(1-az-1)423.--k4ak-1(1-az-1)24.-a cos k r1+az-1x(t)=0fort<0x(kT)=x(k)=0fork<0Unless otherwise noted, k=0,1,2,3