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== 1. Linearity == | == 1. Linearity == | ||
| − | <span class="texhtml">''Z''(''a''''x'''''<b>[''n''] + ''b'''''y''[''n'']) = ''a''''X'''''<b>(</b>'''''z'') + ''b''''''''Y''(''z'')</span>''' | + | <span class="texhtml">''Z''(''a''''x'''''<b>[''n''] + ''b'''''y''[''n'']) = ''a''''X'''''<b>(</b>'''''z'') + ''b''''''''Y''(''z'')</span>''' |
== 2. Time Delay == | == 2. Time Delay == | ||
Latest revision as of 18:10, 16 December 2010
== 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>
