# Questions tagged [z-transform]

The Z-transform converts a discrete time-domain signal, which is a sequence of real or complex numbers, into a complex frequency-domain representation.

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### Z Transform and Difference Equation [closed]

Given that $$H(Z) = 4z+2/(4z^2+2)*(2z-1).$$ Find the difference equation of g(n) such that g(n) and h(n) are two cascading filter such that output is same as input. Moreover find the frequency ...
1 vote
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### What can be the pole zero diagram [closed]

Does the pole zero plot for $$H(z)=(1-z^{-1})^3(1+z^{-1})^3$$ have 6 poles at origin and 3 zeroes at 1? Just answer yes or no, not your homework question knowledge
1 vote
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### For unit step $g(t) = u(t)$, why does $G(z) = \frac{z}{1-z}$, whereas $G(s) = \frac{1}{s}$?

Edit: The source of my confusion is over the existence of multiple s-z mappings. After researching these mappings and where they came from, I couldn't find why $z=e^{sT}$ can be ignored and replaced ...
39 views

### Function Transfer of Block Diagram Discrete System

I need to find out the transfer function in Z from this diagram, how can I extract this information from this diagram Obs: Doing the math, my H_z gave, H_z = 1 + 0.5z^-1 + 2z^-2 + 2z^-3 + 0.5z^-4 + z^-...
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### How does function c2d in MATLAB manage fractional delay?

the function c2d allows to convert a continuous laplace transfer function to a discrete z-transform transfer function. The base method is the Zero Order Holder. In example: ...
63 views

### Inverse $\mathcal{Z}$-transform of a shifted Dirac delta function $\delta(z - z_{0})$

I'm looking for the inverse $\mathcal{Z}$-transform of a shifted Dirac delta function in the $z$ domain, i.e. $$x[n] = \mathcal{Z}^{-1} \{ \delta(z - z_{0}) \} = \ldots$$ Does an analytic/closed-...
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### Formant bandwidths

I have some intuition about bandwidths from these videos (1 and 2) explaining how the frequency response corresponds to the Z-surface. The only thing I could find on the internet about calculating the ...
171 views

### Impulse Response for an Input-Output Pair

Given an input-output pair of a LTI system \begin{gather*} x[ n] \ =\ 2\delta [ n+2] -\delta [ n+1] +\delta [ n-1]\\ y[ n] \ =\ 4 \delta [ n+2] +\ 4\delta [ n+1] -\delta [ n-1] \end{gather*} My ...
114 views

### Why is the condition: region of convergence of z-transform contains unit circle sufficient for BIBO stability of a discrete time system

I'm reading Signals and Systems by Oppenheim, and in the section 10.7.2 about stability there's a conclusion I don't understand: For the impulse response h[n] of a discrete time system he summarizes: ...
1 vote
79 views

### Not getting the same step response from Laplace transform and it's respective difference equation

I am trying to simulate a plant on a microcontroller. The transfer function of the plant is $$G_{p} \left( s \right) = \frac{2}{\left( s + 3 \right) \left( s - 1 \right)} \tag{1} \label{1}$$ The step ...
1 vote
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### Computing frequency response of a filter given Z-transform

I am currently working on a project that involves analyzing the frequency response $H(e^{j\omega})$ of the filter $H(z)= \frac{1}{2} (1+z^{-1})$. However, I am unsure about the specific steps and ...
1 vote
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### Z-Transform of a Precoder with XOR

I am reading a paper called "Design and Comparison of Three 20-Gb/s Backplane Transceivers for Duobinary, PAM4, and NRZ Data" and got stuck on seemingly easy thing, how the Z-domain ...
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### Condition for Causality

I found, as rule of thumb, that a system is causal and stable when it poles lies inside the unit circle. However, more generally we should argue with region of convergence here, like in this example ...
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### Is there a stable linear shift invariant system whose transfer function is $H(z) = z^*$

I couldn't find such a system but I have also not been able to prove otherwise. Firstly, I don't know exactly how to take the inverse Z-Transform of $z^*$. Secondly, I don't know the ROC associated ... 40 views

### Converting simulink PID block to C code

I have implemented and tuned a PID block in a simulink model and now i want to convert this block to C code to use on my micro controller I have taken the discrete equation of the PID block and the ...
1 vote
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### How can I solve such an inverse Z-transform?

I was going through some old exams and found this question: Find the inverse $Z$-transform of $z^{-1/2}$. I tried using the properties table, but I couldn't find a single useful property that would ... 99 views

### Why does the discrete bode plot look like the following and if possible explain the black vertical line at the end for an averaging filter

Why in the attached image for a simple 3 point moving average that has been converted into a TF (z domain) is there a wired dip? It seems that when I change the sampling time, the dip shifts to the ...
1 vote
110 views

1 vote
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