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.

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Confusion in property of Z transform of ideal sampled waveform

I was reading about z transfom of ideal sampled signals and one of the properties of Z transform of sampled signal that surprised me,here it is (image) So here this property of Z transform is quite ...
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Alternative function for MatLab iztrans to Octave?

I am trying to compute the reverse Z transform on Ocatve and I get the following error: error: 'iztrans' undefined near line 1, column 1 The code I am running is ...
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Summations in Z-Transform

I'm currently working on a problem that involves a Z-Transform. Basically, the essence of the problem is that if: \begin{equation} H\left(z\right) = \sum_{n=0}^{N-1}h\left(n\right)z^{-n} \end{equation}...
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What is the Z-transform of $0.8^{n+2}u(n-1)$?

I have 2 signals. One is $x(n)=(-0.5)^nu(n)$ and the other one is $y(n)=0.8^{n+2}u(n-1)$. I know that for the first one it is $X(z)= 1/(1+0.5z^{-1})$, but what about the other one? I know $y(n)$ is ...
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51 views

Calculating IIR Filter gain at given frequency

Let's consider an IIR filter with transfer function: $H(z)$. Given the sampling frequency $F_s$ how can I calculate gain at say $F$ ? When I was dealing with analog systems when I wanted to calculate ...
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54 views

Can time-invariance be determined from a given a transfer function?

I've the following function. $$ G(z) = 2 + \frac{-1+5z^{-1}}{(1-0.5z^{-1})(1-z^{-1})}$$ Calculating it's inverse using $\mathcal Z$-Transform, I get the following function: $$g[n] = 2\delta[n] + 8u[n] ...
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Determine causality and stability from given filter structure

I have the diagram above. I found the transfer function below from it; The question asks me to find out if the system is causal and stable, but didn't it have to indicate whether it was left-sided or ...
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Is there a simpler way to calculate the amplitude response of the following filter

I would like to calculate the amplitude response $|H(z)|$, $z=e^{j\omega}$, of the following filter: $$H(z)=\frac{\frac{b}{2}+z^{-2}}{2+bz^{-2}}$$ and I would like to avoid using Euler's formula and ...
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Convolution that outputs a unit impulse

Im thinking whether any convolutional operation can output a unit impulse, an example to further explain: where a convolution between system $h[n]$ and unknown system $g[n]$ would output $\delta[n]$. ...
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Z-transform of a cosine without a unit step [duplicate]

What is the $\mathcal Z$-transform of a cosine without a unit step, i.e. $x[n] = \cos(\omega_0 n)$ and not $x[n] = \cos(\omega_0n)u[n]$?
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Z transform of finite signals

I was trying to solve the Z-transform for u[n] - u[n-N], where u[n] means discrete unit step function, and N is some finite integer. I solved this using 2 methods. ...
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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 ...
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38 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 ...
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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?
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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.
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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 ...
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Unilateral Z transform

I tried to calculate the unilateral Z transform of x[n-2], is it right?
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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 ...
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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 ...
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294 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 ...
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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?
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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 $...
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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 ...
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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{-...
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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) = ...
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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 ...
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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 ...
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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 ...
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109 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 ...
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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 ...
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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: ...
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Z transform getting different answer for transform of rational function

Why am i getting different answers and which one is correct?? In this also
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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 ...
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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.
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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 ...
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45 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 ...
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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 ...
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157 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 ?
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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 ...
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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 ...
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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(...
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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.
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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 ...
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330 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 ...
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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 ...
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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, ...
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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) = ...
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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 ...
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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 ...
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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)/(...

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