Howtosignalprocessing
- What is the Z-transform of the polynomial function?
- What is the condition for Z-transform to exist?
- What is the difference between Laplace and Z-transform?
- What are the different methods of evaluating inverse Z-transform?
What is the Z-transform of the polynomial function?
Z-TRANSFORM OF SOME SIMPLE SIGNALS
is a "rational function", that is, a ratio of polynomials. We can characterize it by its zeros (the roots of the numerator) and its poles (the roots of the denominator). In this case there is one zero (z = 0) and one pole (z=a).
What is the condition for Z-transform to exist?
For stability the ROC must contain the unit circle. If we need a causal system then the ROC must contain infinity and the system function will be a right-sided sequence. If we need an anticausal system then the ROC must contain the origin and the system function will be a left-sided sequence.
What is the difference between Laplace and Z-transform?
The Z-transform is used to analyse the discrete-time LTI (also called LSI - Linear Shift Invariant) systems. The Laplace transform is used to analyse the continuous-time LTI systems. The ZT converts the time-domain difference equations into the algebraic equations in z-domain.
What are the different methods of evaluating inverse Z-transform?
There are at least 4 different methods to do this: Inspection. Partial-Fraction Expansion. Power Series Expansion.
