Questions tagged [z-transform]
Questions regarding or involving Z or Inverse Z Transforms with respect to Electrical Engineering.
28
questions
0
votes
1answer
34 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 ...
0
votes
0answers
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 ...
0
votes
0answers
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^{...
0
votes
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?
...
0
votes
1answer
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 ...
4
votes
2answers
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) ...
1
vote
0answers
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 ...
1
vote
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 ...
0
votes
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 ...
0
votes
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 ...
-1
votes
1answer
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?
0
votes
1answer
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 ...
1
vote
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 ...
1
vote
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 ...
0
votes
1answer
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 ...
0
votes
0answers
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)\...
0
votes
0answers
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. ...
0
votes
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....
0
votes
0answers
86 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 ...
2
votes
2answers
1k 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 ...
0
votes
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.
...
1
vote
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
$$X(z)=Z[u(-n+1)] =
\sum_{n=-\infty}^1 z^{-n} =\sum_{n=-1}^\infty z^n = z^{-1} + \sum_{n=0}^\infty z^...
0
votes
1answer
1k views
The process of implementing a discrete model in C++/Arduino
I have developed an embedded electronics system centered around the Arduino Due. In my application, I am controlling the force of the end effector of a rigid object using a DC motor. The feedback ...
0
votes
1answer
283 views
inverse Z-transform: 2z^2(-1/(z-.5)+1/(z-1))
Find x[n]
[]1
this is my solution, however the textbook solution is different and I was wondering what did i did wrong.
this is the textbook solution
Thank you
-4
votes
2answers
7k views
Euler's relation (e^(j*pi/4)
I am doing EE hw right now while going over my notes, I notice that my prof said that e^(jpi/4) = 1 but how?
Using Euler's, I would get e(jpi/4) = cos(pi/4) + jsin(pi/4) = 0.7071 + j0.7071
0
votes
1answer
3k views
Z Transform How to Handle the Inital Condition
I have a question about the Z transform Z{x[k+1]} = X(z)z^1. How do I account for the initial condition? In continuous systems, the analogous situation is L{x'(t)} = sX(s) -x(0). I have a equation ...
1
vote
2answers
16k views
Zero-order hold discretization?
I have some difficulties understanding something. There are several discretization methods, such as zero-order-hold (ZOH), forward euler, backward euler, tustin, et cetera.
Forward euler, backward ...
0
votes
1answer
78 views
Inverze z transform - contour integration
Here is my task:
Find inverse z transform of
$$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 ...
