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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 ...
kile's user avatar
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108 views

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 ...
user22360489's user avatar
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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-...
Mr Phase Locked Loop's user avatar
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0 answers
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?
Adi Goyte's user avatar
4 votes
2 answers
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 ...
Dinh Thong's user avatar
3 votes
0 answers
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 ...
Algo's user avatar
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1 answer
65 views

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": ...
ElectronicsStudent's user avatar
3 votes
2 answers
346 views

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: $$H(z)=\frac{1}{1-\frac{5}{6}z^{-1}+\frac{1}{6}z^{-2}}$$
uncutappleslices's user avatar
5 votes
2 answers
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 ...
Jackson Kaplan's user avatar
0 votes
2 answers
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 ...
vram's user avatar
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1 answer
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Extracting Transient Response from a Rational Transfer Function

I am reading an online book on digital filters and wanted to know how the transient response can be obtained from a rational transfer function. $$\frac{b(1) + b(2)z^{-1} + \cdots + b(n_b+1)z^{-n_b}}{...
shashashamti2008's user avatar
1 vote
0 answers
89 views

What can I conclude about the ROC of a transfer function in discrete time

I have a discrete system with transfer function $$ H\left(z\right)=\frac{a_{2}b_{2}z^{-2}+\left(b_{2}a_{1}+b_{1}\right)z^{-1}+\left(b_{0}+b_{2}\right)}{a_{2}z^{-2}+a_{1}z^{-1}+1} $$ Where \$ a_1,a_2,...
DirichletIsaPartyPooper's user avatar
0 votes
1 answer
66 views

Question about inverse Z-Transform

Assume I a discrete signal with Z-transform $$ \frac{Z^{N+1}-1}{Z^{N+1}-Z^{N}} $$ Is there a reasonable way to know all the possible options for the original discrete signal? (we do not know the ROC, ...
FreeZe's user avatar
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1 vote
1 answer
50 views

Compensation Loop of a mixed system

I have a system which is a mixed system. The system is an analog and numerical system. I modelized the analog part and I know its transfer function which I do not want to modify. The numerical part is ...
Jess's user avatar
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0 votes
1 answer
92 views

K-path sampling transfer function

I'm trying to derive the overall Z-transform for the K-path sampling system shown below from Baker's CMOS Mixed-Signal Circuit Design. I numbered some of the equations that I'll reference. The full ...
Halleff's user avatar
  • 667
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0 answers
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Laplace transform to Z-transform for filter design

I was given an answer to the following question I can't understand, that how is the Impulse Invariance transformation of $$\frac{(s+a)}{(s+a+jb)(s+a-jb)}$$ is $$\frac{(1-e^{-aT} cos(bT) z^{-1})}{(1-e^{...
S.M Rifat Ibn Musa's user avatar
0 votes
2 answers
158 views

Is my Inverse z-transform solution method accurate?

The question is as follows: The book answer is as follows: However, my approach is as shown below I even cross checked my partial fraction and it was correct. Please tell me where is my mistake? ...
OMAR's user avatar
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1 answer
395 views

What is the stability of a digital signal processed by a filter with z-transform?

I have a question from the book FE Electrical and Computer Review Manual by Michael R. Lindeburg page# DE X-1 with its answer as follows: I tried to solve it as follows: I don't understand why is it ...
OMAR's user avatar
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4 votes
2 answers
1k views

Relation between Fast Fourier Transform and Laplace/Continuous Fourier representation

I am trying to identify a system by means of its differential equation (i.e., Lapace representation). I put together a rather straightforward regression algorithm (similar to Proni's method for ARMA) ...
Edgar Brown's user avatar
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1 vote
0 answers
386 views

How to determine the inverse Z-transform using partial fraction?

Task: Determine the inverse z-transform of a discrete-time system represented by the rational expression below using the partial fraction expansion method. The impulse response of the system is ...
Rose's user avatar
  • 67
1 vote
1 answer
3k views

s-domain to z-domain conversion in MATLAB

I want to convert a transfer function from s-domain to z-domain. But, by keeping variable i.e without assigning values to variables. I tried to do it with s2z command but it demands numeric input, not ...
Uzi.4's user avatar
  • 25
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1 answer
149 views

How can this problem be solved with partial fractions? (Zero order holder with g(s) block function)

im trying to figure out how to solve this problems for values a=2; actually im stuck, professor told me how to work it, but i cant figure out what to do exactly, we are using partial fractions inverse ...
Caesar Cruez's user avatar
0 votes
2 answers
469 views

Inverse z transform using partial fraction

Here's my attempt at an inverse z transform using partial fraction. I was going through my textbook and it stated that all the z terms need to be converted to z inverse before using partial fraction ...
vasiqshair's user avatar
-1 votes
1 answer
92 views

transfer function discrete

If \$f[n]\$ is the input and \$g[n]\$ is the output, how can I determine the transfer function of the diagram?
Benjamin Arce's user avatar
0 votes
1 answer
89 views

Inverse Z-transform Problem [closed]

I'm rather stuck trying to compute the inverse Z-transform y[n] of the function below. I'm having trouble selecting the correct formulas from the table to achieve the right solution. Any help with ...
wwjrmmr's user avatar
  • 23
1 vote
3 answers
2k views

z-Transform Methods: Definition vs. Rectangular Rule or Tustin's Rule

The definition of the z-transform is defined as \$z = e^{sT}\$ where "s" is complex frequency for continuous-time systems and "T" is the sample period. Why are rules such as the forward rectangular ...
Help Appreciated's user avatar
1 vote
2 answers
2k views

Solving Difference Equation Using Z-Transform

I was trying to solve a problem given in my textbook. I have attached the solution given in the book. I thought some modifications where needed to it and tried to solve in a different way. I ended up ...
Nikhil Kashyap's user avatar
0 votes
1 answer
194 views

Same z transformed function, but different answers of inverse z transform?

Given z transformed function is E(z)=1/(z+4) I know there are several ways to get the inverse z transform of this function. use partial fraction E(z)=1/(z+4) E(z)/z=1/z(z+4) apply partial fraction ...
youngjae's user avatar
0 votes
0 answers
348 views

2nd Order transfer function to difference equations

I'm wondering if someone could check to see if my conversion of a standard second order transfer function to a difference equation is correct, and maybe also help with doing a computer implementation. ...
Collaptic's user avatar
  • 113
-1 votes
1 answer
1k views

Calculating discrete-time transfer function

I have a continuous function \begin{equation}G_p(s) = {1\over s^2} \end{equation} which I am trying to combine with a zero order hold (with a sampling time of 1 second) to produce a discrete function....
Ca01an's user avatar
  • 105
0 votes
0 answers
97 views

Determining final value of the output of a discrete system

I'm going through an exam question where I've been told that the samples f(kT) of the following function \begin{equation}{\text{F}\left(z\right)=\frac{1}{1-0.819z^{-1}}} \end{equation} are applied to ...
Ca01an's user avatar
  • 105
2 votes
2 answers
2k views

Calculating the pulse transfer function

I've been tasked with showing that the pulse transfer function G(z) of the following plant \begin{equation}G_p(s) = {12\over (s+1)(s+4)} \end{equation} being sampled and held by a zero order hold ...
Ca01an's user avatar
  • 105
0 votes
1 answer
2k views

Calculating pulse transfer function

I've been tasked with finding the pulse transfer function G(z) of the combination of the following equation \begin{equation}G_p(s) = {10\over (s+1)(s+2)(s+3)} \end{equation} and a zero order hold. ...
Ca01an's user avatar
  • 105
1 vote
1 answer
4k views

ROC of z transform of u(-n+1)

I am having confusion regarding ROC of z transform of u(-n+1) z transform of u(-n+1) is given by $$X(z)=Z[u(-n+1)] = \sum_{n=-\infty}^1 z^{-n} =\sum_{n=-1}^\infty z^n = z^{-1} + \sum_{n=0}^\infty z^...
Soumee's user avatar
  • 313
0 votes
1 answer
2k views

The process of implementing a discrete model in C++/Arduino

I have developed an embedded electronics system centered around the Arduino Due. In my application, I am controlling the force of the end effector of a rigid object using a DC motor. The feedback ...
gelman_grad's user avatar
0 votes
1 answer
413 views

inverse Z-transform: 2z^2(-1/(z-.5)+1/(z-1))

Find x[n] []1 this is my solution, however the textbook solution is different and I was wondering what did i did wrong. this is the textbook solution Thank you
JavaBeginner's user avatar
-4 votes
2 answers
13k views

Euler's relation (e^(j*pi/4)

I am doing EE hw right now while going over my notes, I notice that my prof said that e^(jpi/4) = 1 but how? Using Euler's, I would get e(jpi/4) = cos(pi/4) + jsin(pi/4) = 0.7071 + j0.7071
JavaBeginner's user avatar
0 votes
1 answer
5k views

Z Transform How to Handle the Inital Condition

I have a question about the Z transform Z{x[k+1]} = X(z)z^1. How do I account for the initial condition? In continuous systems, the analogous situation is L{x'(t)} = sX(s) -x(0). I have a equation ...
bud's user avatar
  • 143
2 votes
2 answers
23k views

Zero-order hold discretization?

I have some difficulties understanding something. There are several discretization methods, such as zero-order-hold (ZOH), forward euler, backward euler, tustin, et cetera. Forward euler, backward ...
WG-'s user avatar
  • 161
0 votes
1 answer
95 views

Inverze z transform - contour integration

Here is my task: Find inverse z transform of $$X(z)=\frac{1}{2-3z}$$ if \$ |z|>\frac{2}{3} \$ using definition formula. I found that $$x(n) = \frac{1}{3}(\frac{2}{3})^{n-1}u(n-1)$$ (using ...
etf's user avatar
  • 115