# 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 stability

What is the causality & stability status for three cases shown (aso in attached photo) ? $$H(z) = \frac{z(z-1)}{(z+1)(z+\frac{1}{3})}$$ for three possible regions of convergence as: a-) |z| > ...
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### How to determine poles and zeros of the z-transform?

This is a simple question, but I just don't understand how we determine the poles and zeros of a rational system function. For example, for the LTI system described by this constant coefficient ...
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### How does an IIR system affect magnitude and phase of a sinusoidal signal

Consider an IIR system with impulse response $h[n]=\left( \frac{1}{\sqrt{3}} \right)^n u[n]$. If I apply $x[n]=\cos(n \frac{\pi}{2} + \varphi)$ at the input, how can I determine the change in ...
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### Transfer function of resonant filter with 2 poles, peak at $f_0 = 500\text{ Hz}$, and $\Delta f = 32\text{ Hz}$

This a contest question. I'd like some help because I can't find any materials related to this topic. https://www.qconcursos.com/questoes-de-concursos/questao/ecd6c966-51 My english translation: ...
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### transfer function and 'causal' signal - evaluate transfer function or use z-transform of input?

From my studying difference equations and transfer functions, I understand that when a complex exponential input $x[n]=z_1^n$ is applied to an LTI system with transfer function $H(z)$, determining the ...
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### How to compute impulse and frequency response of Flanger?

I have to the implementation of a Flanger effect on Matlab, buy previously I have to plot its frequency response and impulse response. The difference equation is $y[n]=x[n]+a\cdot x[n-d[n]]$ where $a$...
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### Determine the stability of a system without using the $\mathcal Z$-transform (described by a difference equation)

For example, let's say a causal LTI System is described by the following equation: $$y[n] - ay[n-1] = x[n] - bx[n-1],\quad n \in Z$$ Is there a way to determine (in this case) the stability of the ...
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### Where does this star came from? [EDIT - Detailed Question]

First of all, it's a rare topic in google, so I can't find intuitive explanation about step-invariant, so I don't understand actually what it is, except to solve zero order hold transfer function. In ...
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### Marginal Stability based on Poles

We know that a discrete-time system with a (Z-transform) transfer function that has a pole of magnitude 1 (i.e. $|z|=1$ is a pole of the transfer function) is marginally stable if the pole at $z=1$ is ...
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### How do I find the ROC of a system if it has no poles

The output of a system of discrete time $y[n]$ is corellated with the input $x[n]$ through the equation $y[n]$. $$y[n] = \frac 13\big(x[n-1]+x[n]+x[n+1]\big)$$ It then asks me to find the system ...
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### Relation between time domain, DTFT domain and frequency domain

Problem The sampling frequency of a continuous-time signal is $S$ kHz, what does $\frac{\pi}{4}$ radians/sample in DTFT domain represent in Hz in frequency domain? Prove the relationship. Doubts I ...