Questions tagged [z-transform]

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

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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 ...
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35 views

Help with basic discretization of a linear system

With a \$T\$ period discretization on the feedback and a first order hold after it. I believe this is a hybrid system because I imagine it's output to have both discrete and continuous behavior. How ...
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28 views

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^{...
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2answers
65 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? ...
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64 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 ...
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179 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) ...
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43 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 ...
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1answer
213 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 ...
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1answer
48 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 ...
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2answers
77 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 ...
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73 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?
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58 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 ...
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3answers
954 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 ...
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2answers
973 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 ...
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135 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 ...
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262 views

How to find Z Transform of the function which is on S domain?

Given a $s$ domain function $$F(s)=\frac{3\, e^{-0.2s}+3}{s(s+3)}$$ and i have to find the Z-Transform of the function for (1)T=0.1 sec (2) T=0.3 sec For T=0.1 sec i can write $$ 3(e^{-0.2s}+1)\...
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259 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. ...
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1answer
273 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....
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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 ...
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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 ...
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1answer
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. ...
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1answer
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^...
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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 ...
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1answer
283 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
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2answers
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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
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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 ...
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2answers
16k 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 ...
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1answer
78 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 ...