Properties - Rhea

== Properties of Z transform ==

1. Linearity

<span class="texhtml">Z(a'x<b>[n] + by[n]) = a'X<b>(</b>z) + b'''Y(z)</span>

2. Time Delay

<math>Z(x[n-k])=z^{-k}[X(z)+\sum_{n=1}^{k}x[-n]z^{n}]</math>

3. Time Advance

<math>Z(x[n+k])=z^{k}[X(z)-\sum_{n=0}^{k-1}x[n]z^{-n}]</math>

4. Time Convolution Theorem

<span class="texhtml">Z(x[n] * y[n]) = X(z)Y(z)</span>