(New page: <br>== Properties of Z transform == == 1. Linearity == <span class="texhtml">''Z''(''a''''x'''''<b>[''n''] + ''b'''''y''[''n'']) = ''a''''X'''''<b>(</b>'''''z'') ...) |
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| − | <br>== Properties of Z transform == | + | <br>== Properties of Z transform == |
| − | == 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 == |
<math>Z(x[n-k])=z^{-k}[X(z)+\sum_{n=1}^{k}x[-n]z^{n}]</math> | <math>Z(x[n-k])=z^{-k}[X(z)+\sum_{n=1}^{k}x[-n]z^{n}]</math> | ||
| − | == 3. Time Advance == | + | == 3. Time Advance == |
<math>Z(x[n+k])=z^{k}[X(z)-\sum_{n=0}^{k-1}x[n]z^{-n}]</math> | <math>Z(x[n+k])=z^{k}[X(z)-\sum_{n=0}^{k-1}x[n]z^{-n}]</math> | ||
| − | == 4. Time Convolution Theorem == | + | == 4. Time Convolution Theorem == |
<span class="texhtml">''Z''(''x''[''n''] * ''y''[''n'']) = ''X''(''z'')''Y''(''z'')</span> | <span class="texhtml">''Z''(''x''[''n''] * ''y''[''n'']) = ''X''(''z'')''Y''(''z'')</span> | ||
Revision as of 17:49, 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>
