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.
524
questions
0
votes
0
answers
23
views
Z Transform and Difference Equation [closed]
Given that
$$H(Z) = 4z+2/(4z^2+2)*(2z-1).$$
Find the difference equation of g(n) such that g(n) and h(n) are two cascading filter such that output is same as input. Moreover find the frequency ...
1
vote
0
answers
52
views
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
- 21
1
vote
1
answer
96
views
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 ...
0
votes
0
answers
39
views
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^-...
4
votes
1
answer
73
views
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:
...
0
votes
1
answer
63
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-...
0
votes
0
answers
18
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 ...
- 378
2
votes
1
answer
171
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 ...
- 23
3
votes
2
answers
114
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:
...
- 31
1
vote
1
answer
79
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 ...
- 11
1
vote
1
answer
67
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 ...
1
vote
0
answers
39
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 ...
0
votes
2
answers
152
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 ...
- 103
3
votes
2
answers
123
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 ...
user64710
0
votes
0
answers
40
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 ...
1
vote
2
answers
539
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 ...
user64710
0
votes
1
answer
99
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 ...
1
vote
1
answer
110
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 :
$$
\begin{split}
\...
- 487
0
votes
0
answers
35
views
Problem regarding Inverse Z-transformation
I am doing research on time series analysis. I did a z-transform of the function $F(n)$. I get results as
$F(z) = \frac{1}{1-\frac{z^{2}}{(z-a)(z-b)}}$.
I tried to find inverse z-transform to find the ...
1
vote
2
answers
226
views
Factorization of transfer function using its roots
I'm missing a step to understand the factorization of the FIR filter transfer function:
$$H(z)=\sum\limits _{k=0}^{M}b_{k}z^{-k} \tag{1}$$
From DSP First:
The $z$-transform of a finite-length signal, ...
- 433
1
vote
1
answer
191
views
Confusion regarding usage of MATLAB for Z domain?
How we can use MATLAB for z domain especially in scenarios where we have two different expressions of Z transform(one has negative powers of z and other has positive powers of z)
I have added a link ...
- 1,850
0
votes
1
answer
119
views
Inverse Z Transform to Partial Fraction Expansion
I am solving a problem to find the zeros and poles. Subsequently, it is requires to determine the impulse response. Below is the system function:
$H(z)=\tfrac{z}{20z^2-4z+1}$
I am able to compute the ...
- 101
3
votes
0
answers
42
views
Inverting transformation $\displaystyle m(t)=\sum_{i=1}^d x(i)^t$
Suppose there's a vector of $d$ of positive numbers $x(1),\ldots,x(d)$ which I need to obtain from a vector of $d$ derived quantities $m(t_1),\ldots,m(t_d)$ where $\{t_i\}$ is some conveniently chosen ...
- 211
0
votes
0
answers
35
views
Remove over and undershoot from an output signal by manipulating the input
I have an experiment for which I want to generate a high-power short-voltage pulse with no over and undershoot. For this, I am using an amplifier. I set a pulse with the desired width as input (I use ...
- 1
2
votes
1
answer
2k
views
Finding the inverse $z$-transform
I have the transfer function: $$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)}$$
I attempted partial fraction expansion in order to ...
- 33
0
votes
1
answer
43
views
Do a pole/zero plot and specified ROC uniquely define an inverse z-transform?
I know that if I have a closed-form algebraic expression $X(z)$ and I specify the region of convergence, this uniquely identifies exactly time-domain sequence (inverse Z-transform) $x[n]$.
Let's ...
- 3
0
votes
0
answers
67
views
Find the equation of y[n] from the block diagram
So we are given a block diagram and we have to find the y[n] "equation". The problem is i just dont get what that plus at the end does
Also i have "calculated" the equation but id ...
- 111
1
vote
1
answer
41
views
LTI system: can I infer the system is causal based only on the transfer function without the ROC?
Suppose we have an linear time-invariant (LTI) system which acts on discrete signals. Suppose someone tells us the transfer function is: $$H(z) = \frac{1}{z-2},$$ but doesn't specify the ROC. Now the ...
- 13
1
vote
1
answer
60
views
Invertible system for the eigenfunction $x[n]=e^{j\omega n}$
I was doing some calculations in my LTI systems course and I stumbled in an interesting question I wasn't really sure how to answer so I'd appreciate any direction or solution you can give me:
I'm ...
- 11
0
votes
1
answer
73
views
What type of filter is that?
I have a transfer function in z-plane with two poles and two zeros. I plotted the function with matlab
...
- 239
2
votes
2
answers
135
views
Z - Transform of a non recursive block diagramm
i am currently struggling to find the Transfer Function of the following Block Diagram, since i have never done it for a non recursive System, could somebody please walk me through the process of it?
...
- 23
1
vote
1
answer
63
views
Deducing phase from frequency response $1-z^{-1} $
In Boaz Porat's book about signal proccessing, at part 8 he mentions the example:
$$ 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\...
- 113
1
vote
2
answers
75
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).
$$y[n] ...
0
votes
1
answer
53
views
Transforming $G(z) = z-1$ to time-domain
The $\mathcal{Z}$-transform of a discrete-signal is namely $$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$$
I would be having a ...
- 15
0
votes
2
answers
115
views
How to find zeros of a transfer function
Given the following transfer function,
$$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}{...
- 359
0
votes
1
answer
175
views
Z domain transfer function including time delay to difference equation
How can get the difference equation of a $\mathcal{Z}$-transform transfer function with time delay? How does a time delay influence the difference equation?
For example:
$$H(z) = \frac{8z^{94}}{z-0.9}...
1
vote
1
answer
104
views
Is the Final value theorem applicable for some non-causal signals?
A digital signal $x[n]$ is zero at odd sample numbers and one at even sample numbers.
What will be the value of this Signal at $n = \infty$?
Not exactly sure, but I thought that infinity (as a integer)...
2
votes
2
answers
91
views
Convert filtering source C-code into difference equation
I'm struggling to convert three simple lines of code into a difference equation to calculate the frequency response.
The C-code is as simple (and legacy), as
...
- 135
2
votes
1
answer
106
views
Is the implementation of this Z-transform correct?
I am reviewing the simulation of a control system. One of the system's requirement diagrams currently contains the following:
N-DOT is the shaft acceleration, DT is the update rate in milliseconds. ...
- 123
0
votes
1
answer
40
views
Acausal form of $Z^{-1}\left(\frac{1}{z-a}\right)$
We know that $Z^{-1}\left(\frac{z}{z-a}\right) = a^nu[n]$ if $|z| > |a|$.
In addition, $Z^{-1}\left(\frac{1}{z-a}\right) = a^{n-1}u[n-1]$ if $|z| > |a|$. This is the delayed version of the first ...
- 31
1
vote
2
answers
187
views
How does Power Spectrum remain symmetric in Z domain?
Can you tell me how the $P_x(z)=P_x^*(1/z^*)$ is mathematically correct. I can understand the $P_x(e^{jw})=P_x^*(e^{jw})$ as $P_x$ is real value. But why take the Z domain representation in this way ($...
0
votes
1
answer
58
views
finding x[0] from the region of convergence
I have the ROC of a signal $x[n]$ with $z$-transform $X(z)$ as below:
Now I am wondering how I can find $x[0]$ by not calculating inverse z transform based on the roc, I am looking for a simpler, and ...
- 11
2
votes
1
answer
245
views
Cascade of Downsample and Upsample
Consider a cascade involving a downsampler (factor $M$) and an upsampler (factor $L$). For the sequence
$$x[n] \rightarrow D \xrightarrow{{v_{1}[n]}} U \rightarrow y[n]$$
where $D$ denotes ...
- 359
0
votes
1
answer
68
views
Examine the operation of a filter, given its z-transform
I am given the z-transform of a filter $$H(z) = \frac{z^2 - 1}{(z-z_1)(z-z_2)(z-z_3)(z-z_4)}$$
where $z_1^* = z_2$, and $z_3^* = z_4$. I'm interested in the operation of this filter, and what happens ...
- 147
0
votes
0
answers
108
views
Impulse response from the transfer function
The discrete system has poles at points $z_{1,2} = 0.8e^{\pm{i\pi /6}}$ and $z_{3,4}=0.8e^{\pm{i\pi/2}}$, and two-fold zeros at $1$ and $-1$. The task is to determine the impulse response of the ...
- 147
1
vote
1
answer
193
views
Multirate Control System Transfer Functions
I'm interested in oversampling the inputs to a digital controller to increase the SNR of the input process variable signal. I've read on this site and in articles like the one below that it is not ...
- 266
2
votes
1
answer
323
views
Different PI controller implementations and their respective discrete transfer functions
So I need to implement a PI-controller and I found an Implementation of an PID-controller with some background explanation. I adapted the implementation to an PI-controller, implemented it and got the ...
- 23
0
votes
0
answers
93
views
Z-Transform of a Complex Number
I have a more general question about $z$-transforms that I am having difficulty finding an answer to.
Suppose we have a two-sided sequence something along the lines of:
$$x(n)=a^{|n|}$$
where $a \in \...
- 1
0
votes
1
answer
145
views
What is causal inverse of a system?
Let's say that I have a system $H(z)$. What is causal inverse and how do I compute the causal inverse of $H(z)$?
2
votes
1
answer
350
views
Sampling with impulse train
There are many times when the textbooks used by all university students like me make an introduction to the notion of sampling of a continuous-time signal with an impulse train as shown below.
Why do ...
