Referencia: Schaum Hsu Tabla 4-2 p173. Lathi Tabla 5.2 p509. Oppenheim Tabla 10.3 p793
| Propiedad | señal | Transformada z | ROC |
|---|---|---|---|
| x[n] x1[n] x2[n] |
X[z] X1[z] X2[z] |
R R1 R2 |
|
| Aditiva | x1[n] + x2[n] | X1[z] + X2[z] | |
| Escalabilidad | a x[n] | a X[z] | |
| Linealidad | a_1 x_1[n] + a_2 x_2[n] | a_1 X_1[z] + a_2 X_2[z] | R’ ⊃R1∩R2 |
| Desplazamiento en tiempo |
x[n-n0] | z-n0 X[z] | R’ ⊃ R∩{0<|z|<∞} |
| Multiplicación por z0n |
z0n x[n] | X \big(\frac{z}{z_0}\big) | R’ = |z0|R |
| Multiplicación por ejβn |
ejβn x[n] | X(e-jβ z) | R’ = R |
| Inversión en tiempo | x[-n] | X \big(\frac{1}{z}\big) | R’ = 1/R |
| Multiplicación por n |
n x[n] | -z \frac{\delta}{\delta z}X(z) | R’ = R |
| Acumulativa | \sum_{k=-\infty}^n x[n] | \frac{1}{1-z^{-1}} X(z) | R’ ⊃ R∩{|z|>1} |
| Convolución | x_1 \circledast z_2 | X1[z]X2[z] | R’ ⊃R1∩R2 |
| Valor inicial | x[0] | \lim _{z \rightarrow \infty} X[z] | |
| Valor Final | \lim _{N \rightarrow \infty} x[N] | \lim _{z \rightarrow 1} (z-1) X[z] | |
| polos de (z-1)X[z] dentro de círculo unitario | |||