Z变换的性质

x(t)或x(k)

Z[x(t)]或Z[x(k)]

αx(t)

αX(z)

x_i(t)+x₂(t)

X₁(z)+X₂(z)

x(t+T)或x(k+1)

zX(z)-zx(0)

x(t+2T)

z²X(z)-z²x(0)-zx(T)

x(k+2)

z²X(z)-z²x(0)-zx(1)

x(t+kT)

x^kX(z)-z^kx(0)-z^k-1x(T)-…-zx(kT-T)

x(k+m)

z^mX(z)-z^mx(0)-z^m-1x(1)…-zx(m-1)

tx(t)

kx(k)

e^-αtx(t)

X(ze^αT)

e^-αkx(k)

X(ze^α)

α^kx(k)

kα^kx(k)

x(0)

x(∞)

X(1)

X(z)Y(z)