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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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As the ROC, both of r<1 and r>1 can be the answer?

I have to find the range of r which makes H(z) stable. There is no restriction of left sided or right sided. Then, both r<1 (z>r) and r > 1 can be the answer?
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51 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
153 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
551 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 ...
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1answer
101 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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247 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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180 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
89 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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73 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 ...
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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 ...
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1answer
1k 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
2k 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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805 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 ...
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1answer
191 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
4k 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
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2k 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 ...
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2answers
11k 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
74 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 ...