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.

Filter by
Sorted by
Tagged with
0
votes
1answer
17 views

Frequency response of filter <-> signal mix

This might be a weird question but here's the setup: I have a few biquads that filter a signal $x[n]$ and output the filtered signal $y[n]$. I can calculate the frequency response of those biquads ...
1
vote
1answer
28 views

Determine the Z-Transform for the following sequence: $ |n|(\frac{1}{2})^{|n|} $

Determine the Z-Transform for the following sequence: $$ |n|(\frac{1}{2})^{|n|} $$ I have tried to solve the above problem. However, the answer that I got is the negative of what is given in the ...
0
votes
1answer
26 views

Finding inverse Z Transform

Find the inverse Z transform: I have done the solution but my answer does not match with the one given in the textbook. What I may have done wrong?
0
votes
1answer
18 views

How to determine whether a filter is high/low or band pass from the Z transform?

How to solve questions of these kind? I have tried by replacing $z=re^{jw}$ and taking the limits from $0$ to $\infty$. But I am not sure what $e^{j\infty}$ is.
0
votes
2answers
26 views

Average image over $N$ frames with one frame buffer

Can you give some filter that is averaging an image over $N$ samples in a recursive way that only needs one frame buffer? $\frac{1}{N} \sum_{k=1}^{N} y_{k}(m,n)$ I can only imagine filters that need ...
0
votes
1answer
27 views

Unilateral Z transform

I tried to calculate the unilateral Z transform of x[n-2], is it right?
1
vote
2answers
58 views

On the stability and causality of a discrete system

On MIT's open course a simple exercise with two questions is given. On the first part, they question about the properties of the following discrete system: $$ y[n]=x[n]+0.5y[n−1]−2y[n−2] $$ The ...
0
votes
1answer
15 views

How to find H(z) and H(k) from a given causal function

Consider the causal function, $y[k] = 2x[k] - 40x[k - 1] + 10y[k - 1]$ 􀀀 $16y[k - 2]$; where $y[k]$ is the output and $x[k]$ is the input. Assume that the system is initially at rest. Please someone ...
0
votes
2answers
102 views

How can I plot the frequency response on a bode diagram with Fast Fourier Transform?

Assume that we have an unknow dynamical system and we only want to estimate its parameters. The system can be discribed as: Continous time: $$G(s) = \frac{3s + 5} {5s^2 + 3s + 2}$$ Discrete time ...
0
votes
3answers
51 views

Z-Transform vs. Fourier Transform convergence

Are there signals for which the Fourier transform is known to exist (perhaps including singularities) and for which the z-transform does not converge?
0
votes
2answers
39 views

Impulse response of an LTI system given the input and output signals

I have been given the input and output signals of an LTI system as: $x[n] = (\frac{1}{2})^nu[n] + 2^nu[-n-1]$ $y[n] = 6(\frac{1}{2})^nu[n] - 6(\frac{3}{4})^nu[n]$ I have found the system function $...
0
votes
1answer
27 views

Do all systems in z domain are filters?

Normally a system transfer function is represented by H(z) I want to know wether all those system transfer functions are only representing a digital filter? Or their any other thing/entity in z ...
0
votes
2answers
45 views

Using ROC to find stability of system in specific example

I've started learning about finding the ROC from the transfer function, but I'm confused about an example. $$H(Z) = \frac{2Z + 1}{Z^2 + Z - \frac{5}{16}}$$ I understand the poles lie at $z = \frac{-...
0
votes
1answer
44 views

Transfer Function Block Diagram Confirmation

Can someone confirm if this is the correct block diagram for the following transfer function? The original equation provided was: y[n+1] = y[n] + 0.01x[n] Which I rearranged into H(z) = Y(z)/X(z) = ...
2
votes
1answer
451 views

When to use Fourier, Laplace and Z transforms?

If we have an LTI system, with an input signal $x(t)$, impulse response $h(t)$ and output $y(t)$, I was under the assumption that if the input and impulse response were continuous in time, then you ...
2
votes
2answers
71 views

In z-transform, if z means “delay”, why do we talk about the value of z?

I've been watching MIT's signals course and trying to understand $z$-transform. The course introduces $z^{-1}$ as an operator that delays the signal by $1$ time unit (which works very well with the ...
2
votes
1answer
68 views

Factored form vs partial fraction form?

I have already understood partial fraction and here is link for my relevant DSP SE question Finding inverse z transform for two sided ROC? But now i want to know, is there any difference between ...
1
vote
3answers
94 views

Is $\cos(\pi \sqrt n)u[n]$ stable?

I took a z transform and got a double pole at $z=1$, but I don't know if that's correct. I'm lost because I don't know if $\cos(\theta)$ converges or diverges or what that means for $h[n]$ being ...
0
votes
3answers
90 views

Necessary Conditions for stability in z domain?

What are the necessary(must) conditions for stability in z domain? I am sure about one(ROC must include unit circle) Is there any other such condition which states that there shouldn't be any poles in ...
0
votes
2answers
57 views

Finding inverse z transform for two sided ROC?

I have a z transform $Y(z)=(z^2-z) /(z^2+1.3z+0.3)$ In this case i have two poles ,one at -0.3 and one at -1.0 I want to find inverse z transform of Y(z) Following is my matlab code: ...
1
vote
1answer
41 views

Z transform getting different answer for transform of rational function

Why am i getting different answers and which one is correct?? In this also
1
vote
1answer
159 views

Determing inverse Z-transform using impulse response?

In Matlab there is a command iztrans for finding inverse Z-transform. But how can we find inverse Z-transform using impulse response? The Matlab command ...
0
votes
1answer
27 views

Book request for Z-Transform

I am at the moment self studying Z-Transform. I need some references on this subject with some applications ( electrical circuits or else). What are good references on this subject. Thanks in advance.
1
vote
1answer
52 views

Causality of z-transform $a^nu[n+1]$

To preface, this is not a homework related question but purely for self-study purposes. I'm try to do the analyse of z-transform of $a^nu[n+1]$. It is clearly a non-causal signal, I try to explain it ...
0
votes
1answer
37 views

Derive the Forward Euler substitution for transfer function

In the book "The control handbook. Volume 1 " by Levine, the author shows that the transfer function: can be aproximated and discretized in the transfer function: using the forwar euler integral ...
0
votes
1answer
33 views

Proof of Forward Euler for discretizing a transfer function

In Levine book "The control handbook" it is shown that, for discretizing a transfer function $\frac{1}{s}$ using Forward Euler i simply have to replace s with $\frac{z-1}{T}$. How can extend the ...
0
votes
1answer
95 views

Forward Euler Discretization

I don't understand why the substitution $s=\frac{z-1}{T}$ allows us to discretize a transfer function from laplace to z-transform through Forward Euler Discretization. Can you explain to me ?
0
votes
2answers
41 views

Non-polynomial Z-transform

My prof said that when a transfer function described by a z-transform is not polynomial, then i can't perform the anti-transformation. But, what does it means to be not polynomial ? Can you explain to ...
1
vote
1answer
38 views

Impulse response of a system in z domain

The question 3-23 in the "Discrete-Time Signal Processing - Second Edition" is: and the solution is: I cannot understand the solution. In the second row of the answer when I multiply (-4) with ...
1
vote
1answer
55 views

why z-transform differentiation is needed?

Find the z-transform and sketch pole-zero plot and ROC for $$x(n)=|n|\left(\frac{1}{2}\right)^{|n|}$$ Right now, i can get the following, $$x(n)=\begin{cases} n(\frac{1}{2})^n, & n \geq 0 \\ -n(...
1
vote
1answer
53 views

Inverse Z transform of a left sided signal [closed]

Please help me to find the impulse response $h(n)$ of a Transfer function $H(z) = \dfrac{1+\frac{1}{6}z^{-1}}{1-\frac{1}{4}z^{-1}}$ given $h(n)$ is left sided.
0
votes
1answer
28 views

Effect of sign change on ROC & z transform?

When we take ztransform of unit step it is z/[z-1] And our ROC is |z|>1 But if some how the minus sign between z and 1 changes to +, will our ROC still be same as old ( |z| >1 ) or will it be ...
0
votes
2answers
202 views

LCCDE in simple words?

What is LCCDE?I only know its abbreviation/full form :linear constant-coefficient difference equation I know that in s domain we have differential equations and in z domain we have difference ...
1
vote
1answer
36 views

How we can find ROC(Region of convergence) given a signal in z domain?

I read that ROC is a region,which is a set of values where z transform is defined ,that is it converges Lets say i have a discrete time time signal $x[n]=n^2 u(n)$ and i want to find its ROC(Region ...
0
votes
0answers
26 views

Are discrete time functions expected to be this inaccurate?

I am attempting to test some discrete time functions against their continuous counterparts and I am surprised by how inaccurate the discrete versions are coming out. I am modeling the displacement, ...
0
votes
1answer
47 views

One more inverse z transform … a bit more complicated [closed]

Thank you for all the help teaching me. I am looking at one more inverse z transform and not understanding what to do with it. $F(t) = m \cdot a(t)$ (i.e. Force = mass $\times$ acceleration) $F(s) = ...
0
votes
1answer
18 views

How to do this inverse Z-transform? Is this correct?

It was explained to me here that I need to do an inverse z-transform on a z-based equation in order to get something I can use. That example was quite simple. But I'm not sure how to do the same ...
-1
votes
2answers
86 views

What does z^(-1) represent here?

I understand that when you have a Laplace function, you can do a bilinear or forward/backward Euler substitution for $s$ to phrase it in terms of $z^{-1}$. In a typical filter, $z^{-1}$ represents the ...
0
votes
2answers
39 views

What type of z transform is this?

I am trying to understand this equation: It comes from: $Force = mass * acceleration$ $F(t) = m * a(t)$ $F(s) = m * (s^2 * y(s) - s*y0 - y0)$, where $y0=0$ $F(s) = m * s^2 * y(s)$ $y(s) = F(s)/(...
0
votes
1answer
61 views

ROC of Z Transform of $x(n) = 2(3)^nu(-n)$

Using definition, I got its Z transform as $X(z) = \dfrac{2}{1-\dfrac{z}{3}}$ and the summation converges only when $|z|<\frac{1}{3}$. So its ROC is $|z|<\frac{1}{3}$. But my question is: for ...
1
vote
0answers
25 views

What are the missing steps in the derivation of this equation?

I am trying to understand the model of a piano hammer described here. The relevant excerpt is: As I understand it, they are saying in (12a) that if the hammer spring's uncompressed end's y position ...
4
votes
1answer
61 views

s-Domin or z-Domain - What to Use for Mixed systems

I recently had to deal with a power electronic system where I had to implement a dynamic model of a power converter in order to design a suitable controller for that converter. The control will be ...
2
votes
2answers
352 views

Help with my first (simple) Z-transform

I need to transform this Laplace function to the z-domain: From the answer I received: $s=(1-z^{−1})/T$ Then substitution into my Laplace function would give: $t(z) = 2R/(m*(1-z^{−1})/T + 2R)$ Is ...
0
votes
3answers
69 views

I often see here formula expressed in term of $z$. But what is $z$?

While searching resources for generating pink noise (and with your help in the comments and answers of other questions), I came to such kind of formula: $$ H(z) = { .041 - .096z^{-1} + .051z^{-2} - ...
2
votes
2answers
75 views

How do I convert this simple Laplace equation to Z-domain?

A basic model of coupled strings (eg. piano) is provided here as: The principle is that it has two identical string simulations each formed by a delay line and LPF. The outputs of these are summed at ...
1
vote
1answer
2k views

Is it impossible to determine the inverse Z-transform without any other information?

Suppose I give you this as my transfer function $H(z)$: $$ H(z) = \frac{1} { 1 - az^{-1}}$$ With no other information given, is it even possible to determine the inverse Z-transform? The reason I'...
0
votes
1answer
40 views

How can I obtain the response signal for this question?

In particular I am having trouble with 6b). From what I understand, we can split a difference LTI equation into two sums, the sum of the previous responses, and the sum of the previous inputs. ...
0
votes
1answer
33 views

ROC and impulse response

For the LTI system given below, there are three regions of convergence. $$H(z)=\frac{5-3z^{-1}}{1-\frac53z^{-1}-\frac23z^{-2}}$$ a) Find all possible regions of convergence for this filter. b) For ...
0
votes
0answers
25 views

how do i find the z transfer functions of the two filters?

how do i find the the z transfer functions of the 2 filters? cant seem to derive it . Please help
0
votes
1answer
48 views

Find the length of the impulse response of a Linear Phase Type 4 FIR filter

The length should be found such that the group delay is minimum It is given that the impulse response is real. One zero of the Transfer function is at $0.6e^{j\frac{\pi}{4}}$, and another one is at -...

1
2 3 4 5
8