(New page: ==Definition== The z-Transform is the discrete time analog of the C.T. Laplace Transform. For a D.T. signal <math>x[n]\,</math>, the z-Transform is defined as :<math>X(z) = \sum_{n =...) |
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Any z-Transform will have a realm of convergence. For example, if your signal is: | Any z-Transform will have a realm of convergence. For example, if your signal is: | ||
| − | :<math>x[n] = 2^{n}u[n]</math> | + | :<math>x[n] = 2^{n}u[-n]</math> |
The z-Transform summation reduces to: | The z-Transform summation reduces to: | ||
| − | :<math>\sum_{n = 0}^{\infty} (\frac{ | + | :<math>\sum_{n = 0}^{\infty} (\frac{z}{2})^{n}</math>, which will converge only if <math>|\frac{z}{2}| < 1</math> |
Latest revision as of 19:58, 3 December 2008
Definition
The z-Transform is the discrete time analog of the C.T. Laplace Transform.
For a D.T. signal $ x[n]\, $, the z-Transform is defined as
- $ X(z) = \sum_{n = -\infty}^{\infty} x[n]z^{-n} $
Realm of Convergence
Any z-Transform will have a realm of convergence. For example, if your signal is:
- $ x[n] = 2^{n}u[-n] $
The z-Transform summation reduces to:
- $ \sum_{n = 0}^{\infty} (\frac{z}{2})^{n} $, which will converge only if $ |\frac{z}{2}| < 1 $
