21-04-2012, 10:38 AM
The z-Transform
z-Transform.ppt (Size: 601.5 KB / Downloads: 38)
Introduction
A generalization of Fourier transform
Why generalize it?
FT does not converge on all sequence
Notation good for analysis
Bring the power of complex variable theory deal with the discrete-time signals and systems
Properties of ROC
A ring or disk in the z-plane centered at the origin.
The Fourier Transform of x(n) is converge absolutely iff the ROC includes the unit circle.
The ROC cannot include any poles
Finite Duration Sequences: The ROC is the entire z-plane except possibly z=0 or z=.
Right sided sequences: The ROC extends outward from the outermost finite pole in X(z) to z=.
Left sided sequences: The ROC extends inward from the innermost nonzero pole in X(z) to z=0.
Stable Systems
A stable system requires that its Fourier transform is uniformly convergent.
Fact: Fourier transform is to evaluate z-transform on a unit circle.
A stable system requires the ROC of z-transform to include the unit circle.
Conclusion
Z-transform is very useful in analysis of Digital signal.
And it is very useful in desinging various digital circuits.