Is there a $z$-transform like for variable sampling rate signals?

1. What is the Z-transform of the signal?
2. Where is Z-transform used?
3. Why do we use Z-transform in DSP?
4. What is the Z-transform of the finite duration signal?

What is the Z-transform of the signal?

Definition of Z-Transform

In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency-domain representation. Also, it can be considered as a discrete-time equivalent of the Laplace transform.

Where is Z-transform used?

The Z-transform (ZT) is a mathematical tool which is used to convert the difference equations in time domain into the algebraic equations in z-domain. The Z-transform is a very useful tool in the analysis of a linear shift invariant (LSI) system. An LSI discrete time system is represented by difference equations.

Why do we use Z-transform in DSP?

The Z-Transform is an important tool in DSP that is fundamental to filter design and system analysis. It will help you understand the behavior and stability conditions of a system.

What is the Z-transform of the finite duration signal?

What is the ROC of z-transform of finite duration anti-causal sequence? Explanation: Let us an example of anti causal sequence whose z-transform will be in the form X(z)=1+z+z² which has a finite value at all values of 'z' except at z=∞. So, ROC of an anti-causal sequence is entire z-plane except at z=∞.