Electronics Communication/Signal Processing/Signal Transformation/Z Transform

Z Transform Properties

 * Initial value theorem
 * $$x[0]=\lim_{z\rightarrow \infty}X(z) \ $$, If $$x[n]\,$$ causal


 * Final value theorem
 * $$x[\infty]=\lim_{z\rightarrow 1}(z-1)X(z) \ $$, Only if poles of $$(z-1)X(z) \ $$	 are inside unit circle

Z Transform Table
Here:
 * $$u[n]=1$$ for $$n>=0$$, $$u[n]=0$$ for $$n<0$$
 * $$\delta[n] = 1 $$ for $$n=0$$, $$\delta[n] = 0 $$ otherwise