# Questions tagged [z-transform]

The $z$-transform is a discrete analogue to the Laplace transform, in that it maps a time domain signal into a representation in complex frequency plane.

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### Laplace to Z-transform [closed]

How is the Impulse Invariance transformation of $$\frac{(s+a)}{(s+a+jb)(s+a-jb)}$$ is $$\frac{(1-e^{-aT} cos(bT) z^{-1})}{(1-e^{(-a-jb)T} cos(bT) z^{-1})(1-e^{(-a+jb)T} cos(bT) z^{-1})}$$ ?
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### Z transform or Laplace transform

Is there any app which can perform $z$-transform or can we perform this operation using a scientific calculator?
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### Going in Reverse From Z-Domain to a Difference Equation

I am attempting the task of beginning with a $z$-domain equation, and then reverse engineering a difference equations from it. The eventual goal is to solve the difference equation, and then go back ...
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### Generating Functions VS Z-Transforms as Solutions to Recurrence Relations

In a Discrete Mathematics video, recurrence relations are solved by applying generating functions to each term, doing algebra, and extracting coefficients of the result. There is no mention of Z-...
If we have the sequence $\{1,1,\dots\}$, how would I go about calculating the Z-transform? Such that we find $Z\{1,1 \dots\}(z)$.