# 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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### how to take inverse z transform of 6th order IIR filter

we are told to find coefficients and impulse response of IIR filter of order of 6. There are 6 zeros and 6 poles in the design. Pole and zero pairs are conjugate and poles are within the unit circle ...
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### Discretization of second order ODE, apply Z transform and inverse

I have the following ODE: $\frac{\mathrm{d^2y(t)} }{\mathrm{d} t} + 2\frac{\mathrm{dy(t)} }{\mathrm{d} t}+4y(t)=e^{-2(t-2)}u(t-2)$ With $u(t)$ being the unit step function. I am than asked to ...
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### How did the following factor out to this when doing PFE?

I'm currently applying PFE in getting the Z transform and this was the given: $$X(z) = \frac{z+3}{z^4+6z^3+14z^2+16z+8}$$ Dividing both sides by $z$ it resulted to this: \...
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### Find the z-transform [closed]

I have these expressions for which I need the z-transformed functions. Please help. The Question Expressions My attempt for the first question My attempt for the second question My attempt for the ...
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### What is the Z-transformation of following discrete time signal of this?

I am learning how $Z$-Transforms work, but I have no encountered a situation in which the bound does not account for any signal. Take for example the following discrete time signal: \begin{cases} x(-2)...
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### Recurrence relation with Z-Transform

I'm revising the Z-Transform. I am looking at the book which gives an example of how to solve the recurrence relation $$x_{k+2} - 3x_{k+1} +2x_k = 1$$ where $x_0 = 0$ and $x_1 = 1$. The book uses the ...
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