# Questions tagged [z-transform]

Questions regarding or involving Z or Inverse Z Transforms with respect to Electrical Engineering.

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### What's inverse z transform of $$F(z) = \frac{5} {z-2} - \frac{5} {z-3}$$

Examples from studysmarter said $$F(z) = \frac{5} {z-2} - \frac{5} {z-3}$$ Inverse z transform $$f(n) = 5 \times \Bigl(2^n - 3^n \Bigl)$$ And Google gemini and ChatGPT 3.5 also agrees with ...
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### Help with inverse Z transform

I have the following function on time domain $$f(t) = sin(100 * 2 * \pi * t)$$ and I need to get its discrete values when it's sampled at 1000Hz. After applying the Z transform and using T = 1/1000, I ...
31 views

### Nyquist stability criterion in discrete time domain

I've been transforming systems from the s-domain to the z-domain, and looking at the Nyquist plots I get in the z-domain. So far I've assumed that the Nyquist stability criterion that applies in the s-...
42 views

### Z transform and the magnitude of Fourier transform

Would like to know if the graph of the magnitude in the picture I added is correct. Should I address the other pole?
172 views

### Converting PMSM motor differential equation to difference equation/discrete-time implementation

I am researching about sensorless control of PMSM, and currently looking at how to implement the algorithm into code. From this link Module 9: Position Observer (Part 2/2). I encountered the equations ...
122 views

### LTI system: can I infer the system is causal based only on the transfer function without the ROC?

Suppose we have an linear time-invariant (LTI) system which acts on discrete signals. Suppose someone tells us the transfer function is: $$H(z) = \frac{1}{z-2},$$ but doesn't specify the ROC. Now the ...
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### Z-Transformation Function

I have a system given, which looks like this: simulate this circuit – Schematic created using CircuitLab Now I am task with giving the "difference-equation": ...
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### How to convert this transfer function in the z-domain?

I arrived at: $$\frac{Y[n]}{X[n]}=1-\frac{1}{6}z^{-2}+\frac{5}{6}z^{-1}$$ How do I arrive at: $$H(z)=\frac{1}{1-\frac{5}{6}z^{-1}+\frac{1}{6}z^{-2}}$$
314 views

### Performing block reduction with many takeoff/summing points in sequence

I'm an audio programmer, and I've recently gotten into using transfer functions to model the response of my DSP. However, I've hit a roadblock in trying to reduce a block diagram of one of my DSP ...
260 views

### Can a PI controller be designed by pole placement in the z-plane without transforming the system equations to the state space?

I've some time trying to design a PI controller by pole placement for a BLDC motor, I had basically to study control engineering from zero because I had several years without doing nothing of control ...
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