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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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MATLAB unable to solve Z-transform of dirac delta sequence

I am using MATLAB and trying to find ztransform of dirac(n) which is impulse signal I am studying book Signals and Systems Laboratory with MATLAB Book by Alex Palamides and Anastasia Veloni I have ...
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Confusion regarding Z-transform of unit step sequence in MATLAB

I am using MATLAB and trying to find ztransform of heaviside(n) which is unit step sequence I am studying book Signals and Systems Laboratory with MATLAB Book by Alex Palamides and Anastasia Veloni I ...
DSP_CS's user avatar
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Decay of the impulse response for poles contained in the unit circle

I've been struggling with the following exercise in Ljung's "System Identification: Theory for the User" (Problem 3G.1): Given a rational transfer function $G(z)$ such that its poles are all ...
LSK21's user avatar
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Z-transform of the Unit Step and DTFT

In class we showed the the z transform of the unit step only exists for |z|>1 but we also calculated the DTFT of the unit step. Does convergence on the unit circle imply the DTFT exists but not the ...
Amur's user avatar
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algorithm for second order butterworth filter

I want to implement an algorithm for a second order butterworth filter on the form $ H(s) = \dfrac{Y(s)}{U(s)}= \dfrac{1}{\left(\frac{s}{w_0}\right)^2+2\zeta\frac{s}{w_0}+1} $ I want to get it on the ...
pjoltergeist's user avatar
2 votes
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How to handle non-causality when decomposing a 4th order IIR filter into a parallel bank of second order filters?

What I am trying to do I am trying to code a Gaussian smoothing filter using the 4th order IIR filter described in Van Vliet's paper "Recursive Gaussian derivative filters". My code works ...
Omar Emara's user avatar
1 vote
2 answers
222 views

inverse Z transform for 1/(z-a)

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 ...
kile's user avatar
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The discrete-time impulse response of an IIR filter

Suppose you begin with the following model of a discrete impulse response: $$h[n] = \begin{cases} \displaystyle\sum_{k=1}^K \alpha_k p_k^n & n \ge 0 \\ 0 & n < 0 \end{cases}$$ i.e. a linear ...
DangerousTim's user avatar
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Formants extraction from LPC

I would like to do formants extraction using LPC. I made the necessary pre-emphasis before feeding the speech samples to the LPC function. ...
Anantha Krishnan's user avatar
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1 answer
81 views

Getting two different results when doing Z inverse transform

I saw this question was being asked here a few times, but none got actual answer that helped me ( at other Transform of course ). $$X\left(z\right)=\frac{1-3z^{-1}}{\left(1-0.2z^{-1}\right)\left(1+0....
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Finding inverse $Z$ Transformation of a LTI system and switching of input output signal regarding to difference equation

I have 2 stuffs that are bothering me: I have the equation: $y[n]=8x[n]-2x[n-2]-x[n-4]$ When $x[n]$ input and $y[n]$ output. Now, the system is swapped, $x[n]$ output and $y[n]$ input The difference ...
Ben Shaines's user avatar
1 vote
1 answer
49 views

Confused on the ROC of Z-transform

I'm given a specific function to find its inverse Z-transform. Specifically: $$X(z) = z^3 + \frac{1}{z - 2i} + \frac{1}{z+2i}, |z| > 2 $$ Notice the $|z| >2$. Now what concerns me is the term $z^...
Nyquist-er's user avatar
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How to calculate the accumulation of a signal in the z domain [closed]

I was trying to study for a future DSP exam and while reviewing some questions i was faced with the following: Question 12: Two right-sided discrete-time signals $x \! \left[ n \right]$ and $y \! \...
Ravinala's user avatar
1 vote
1 answer
161 views

2nd order Z transform system [closed]

Related to this. I have been into exploring the world of digital control loop but I have encountered a very simple problem. The unity negative feedback transforms a system which delays a signal by 1 ...
Root Groves's user avatar
2 votes
2 answers
132 views

Laplace transform of this simple parallel RLC circuit? (For audio speaker simulation ...)

SPEAKER AS RLC CIRCUIT I read this article here which demonstrates a simulation of a speaker as a simple RLC circuit where the RLC components are in parallel: MY GOAL I am interested in creating a ...
mike's user avatar
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What is the effect of carrier frequency offset (CFO) on the zeros of the z-transform?

Suppose I have a discrete-time signal vector, for example, x(n)=[1,a1,a2,…,aN]. The signal is then transmitted by using the single carrier pulses, constituting a single-carrier communication over a ...
tuner's user avatar
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1 answer
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Z-Transform of $ x(n+2)u(n) $

I don't know where I went wrong, this might be a dumb question. I am solving for the z-transform of $$ y(n) = x(n+2)u(n) $$. To solve, I used the z-transform equation, $$ Y(z) = \sum_{n=-\infty}^\...
lukasdante's user avatar
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1 answer
249 views

What is damping ratio and natural frequency of z-domain with real negative pole and undifine region

As ilustrated in controlsystemsacademy shown relation between z-domain and s-damain poles by this image. with contour for natural frequency and damping ratio given by these equations. However there ...
M lab's user avatar
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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
Bitsaa's user avatar
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1 answer
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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 ...
ThePhysicsOverthinker's user avatar
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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^-...
Pedrimbus's user avatar
5 votes
1 answer
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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: ...
The Newbie Toad's user avatar
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1 answer
136 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-...
Bart Wolleswinkel's user avatar
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20 views

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 ...
Tom Huntington's user avatar
2 votes
1 answer
233 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 ...
Anmoldeep's user avatar
3 votes
2 answers
300 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: ...
klingeron's user avatar
1 vote
1 answer
96 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 ...
Diptopal's user avatar
1 vote
1 answer
72 views

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 ...
Eminent Emperor Penguin's user avatar
1 vote
0 answers
51 views

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 ...
Mohamed Osama's user avatar
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2 answers
332 views

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 ...
bilaljo's user avatar
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2 answers
130 views

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 ...
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53 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 ...
Boody Alyehia's user avatar
1 vote
2 answers
572 views

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 ...
user avatar
1 vote
1 answer
246 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 ...
George kirby's user avatar
1 vote
1 answer
235 views

What exactly are the assumptions behind Tustin's formula? Application on state space models

I was parsing the forum when I saw this post surging out of the depths of this forum like an old Kraken. The problem is quite simple. You have a continuous time state space model : $$ \begin{split} \...
NokiYola's user avatar
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1 vote
2 answers
349 views

Factorization of transfer function using its roots

I'm missing a step to understand the factorization of the FIR filter transfer function: $$H(z)=\sum\limits _{k=0}^{M}b_{k}z^{-k} \tag{1}$$ From DSP First: The $z$-transform of a finite-length signal, ...
mins's user avatar
  • 463
1 vote
1 answer
224 views

Confusion regarding usage of MATLAB for Z domain?

How we can use MATLAB for z domain especially in scenarios where we have two different expressions of Z transform(one has negative powers of z and other has positive powers of z) I have added a link ...
DSP_CS's user avatar
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1 vote
1 answer
138 views

Inverse Z Transform to Partial Fraction Expansion

I am solving a problem to find the zeros and poles. Subsequently, it is requires to determine the impulse response. Below is the system function: $H(z)=\tfrac{z}{20z^2-4z+1}$ I am able to compute the ...
HaRLoFei's user avatar
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0 answers
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Inverting transformation $\displaystyle m(t)=\sum_{i=1}^d x(i)^t$

Suppose there's a vector of $d$ of positive numbers $x(1),\ldots,x(d)$ which I need to obtain from a vector of $d$ derived quantities $m(t_1),\ldots,m(t_d)$ where $\{t_i\}$ is some conveniently chosen ...
Yaroslav Bulatov's user avatar
2 votes
1 answer
4k views

Finding the inverse $z$-transform

I have the transfer function: $$H(z) = \frac{z^2 + 0.75z + 0.125}{z^2+0.5625}, |z| > 0.75 = \frac{(z-0.5) (z-0.25)}{(z - 0.75j) (z + 0.75 j)}$$ I attempted partial fraction expansion in order to ...
MeljahU's user avatar
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0 votes
1 answer
45 views

Do a pole/zero plot and specified ROC uniquely define an inverse z-transform?

I know that if I have a closed-form algebraic expression $X(z)$ and I specify the region of convergence, this uniquely identifies exactly time-domain sequence (inverse Z-transform) $x[n]$. Let's ...
marlinTJ's user avatar
0 votes
0 answers
77 views

Find the equation of y[n] from the block diagram

So we are given a block diagram and we have to find the y[n] "equation". The problem is i just dont get what that plus at the end does Also i have "calculated" the equation but id ...
Severjan Lici's user avatar
1 vote
1 answer
60 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 ...
Algo's user avatar
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1 vote
1 answer
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Invertible system for the eigenfunction $x[n]=e^{j\omega n}$

I was doing some calculations in my LTI systems course and I stumbled in an interesting question I wasn't really sure how to answer so I'd appreciate any direction or solution you can give me: I'm ...
Daniel's user avatar
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0 votes
1 answer
81 views

What type of filter is that?

I have a transfer function in z-plane with two poles and two zeros. I plotted the function with matlab ...
tonythestark's user avatar
2 votes
2 answers
151 views

Z - Transform of a non recursive block diagramm

i am currently struggling to find the Transfer Function of the following Block Diagram, since i have never done it for a non recursive System, could somebody please walk me through the process of it? ...
ricardo's user avatar
  • 23
1 vote
1 answer
78 views

Deducing phase from frequency response $1-z^{-1} $

In Boaz Porat's book about signal proccessing, at part 8 he mentions the example: $$ H\left(z\right)=1-z^{-1}\Rightarrow H^{f}\left(\theta\right)=1-e^{-j\theta}=\left(e^{\frac{j\theta}{2}}-e^{-\frac{j\...
Danny Blozrov's user avatar
1 vote
2 answers
96 views

Discrete-time system: divergent response to exponential input

I’ve been given the following Difference Equation and tasked with finding the response to $x_0[n] = (-p)^n$ - I’ve managed to $h[n]$ but the convolution itself failed.(The given system is IAR). $$y[n] ...
Piratemetaldrinkingcrew's user avatar
0 votes
1 answer
93 views

Transforming $G(z) = z-1$ to time-domain

The $\mathcal{Z}$-transform of a discrete-signal is namely $$F(z) = \sum_{n=-\infty}^{\infty} f[k] z^{-n}$$ and so if I have a signal in the $\mathcal{Z}$-plane: $$G(z) = z-1$$ I would be having a ...
Meow _J's user avatar
  • 15
0 votes
2 answers
160 views

How to find zeros of a transfer function

Given the following transfer function, $$H(z) = \frac{6 + 4z^{-1}}{2 + 5z^{-1} - 3z^{-2}}$$ How do we find the zeros of the transfer function? We can write the above expression as $$\frac{3(1+\frac{2}{...
MaxFrost's user avatar
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