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Questions tagged [z-transform]

The $z$-transform is a discrete analogue to the Laplace transform, in that it maps a time domain signal into a representation in complex frequency plane.

In mathematics and its applications (notably in signal processing), the $z$-transform is a discrete transformation which maps a time domain signal into a representation in the complex frequency plane.

If $x(n)$ is a time domain signal, then the $z$-transform $X(z)$ of $x(n)$ is given formally by the power series $$X(z)=\sum_{n=-\infty}^\infty x(n)z^{-n}.$$

The $z$-transform has interesting connections to generating functions and the discrete Fourier transform.

303 questions
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What is the concept of Region of Convergence of Z-Transform

I have been trying to learn Z transform. But I haven't found any good source that will clear my concept about the region of convergence. I have found some keywords like unit circle, but I don't have a clear concept about Region of Convergence. I…
Redwanul Sourav
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$z$-transform of $1/n$

How can one calculate the $z$-transform of: $x(n) = \frac{1}{n}$ , where $n \geq 1$? I have searched for table entries, then got stuck while trying to do it with the definition of $z$-transform (summation).
archie
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Weird thing about z-transform and difference

here is my doubt: we were told that the ROC of the Z-transform of the sum of two sequences is the intersection of the respective ROCs as the two of them are limited only if both of them are. Now I had to solve an exercise where I had to compute the…
Baffo rasta
  • 403
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How can I find the inverse Z-transform of $1/z$?

I'm trying to find the sequence ${a_n}$ given the Z-transform $A(z)=1/z$ I'm not sure though how to calculate the inverse transform of $A(z)$, All help is much appreciated
wertyle
  • 43
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How can I find the inverse z transform of 1/(z-a)?

I need to take the inverse z transform of $X(z) = \dfrac{.5}{(z-1)(z-.5)}$. I've used partial fractions to split this into $X(z) = \dfrac{1}{z-.5} - \dfrac{1}{z-1}$ But Here I'm stuck. This isn't in a table, and I'm not sure how to solve it. I've…
Daniel B.
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Suddenly a wild Z-transform appears...

I am attempting to complete the z transform of the following formula: $$x(n) = \frac{1}{2}(n^2+n) u(n-1)$$ I got it into the summation form like so: $$X(z) = \frac{3}{2} \sum_{n=1}^{\infty} n^2(\frac{1}{3} z^{-1})^2 + \frac{3}{2} \sum_{n=1}^{\infty}…
codedude
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Inverse Z-transform with a complex root

The z-transform of a signal is $$ X(z)=\frac{1}{z^2+z+1}$$ I attempted to solve for the the inverse z-transform by decomposing the denominator into complex roots, $\alpha$ and $\alpha^\ast$, to get $$\frac{1}{z^2+z+1} =…
John
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Z transform discrepancy at n=0

I was supposed to find the Inverse z transform of $$\dfrac{1}{(z-5)^3}$$. Approach: I first tried to find out the z transform of $\dfrac{z}{(z-5)^3}$.Partial fraction decomposition tells us: $$\dfrac{z}{(z-5)^3}= \dfrac{-1}{50}\dfrac{5z}{(z-5)^2}…
satan 29
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Help me with z transform

So the question is basically z transform the given system. $(y[n+2] + 3y[n+1] - 4y[n])=(x[n+2] - 5x[n+1])$ I've to find h[z] first then it's really easy to solve it. So that's what I got so far; $z^2y(z) + 3zy(z) - 4y(z) = z^2x(z) -…
L4W
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using z transform pairs to solve the question.

Following is a question about the z transform with: $$ (-\frac{1}{3})^n \, u(-n-2). $$ Now, I know that a transform pair similar to this is: $$ -\alpha^n \, u(-n-1) = \frac{1}{1-\alpha z^{-1}}. $$ Now using that property what I get is: $$…
Muhammad Ahmad
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Finding z transform of this function.

I need to find the z-transform of the function $t^{a}e^{-bt}$. Though it did appear easy to me initially but i cannot figure out how to do so. The problem is that 'a' can be a non-integer. (t can be thought of as a discrete time variable) Can…
user160429
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Z transform of a sequence

Can someone tell me how to find the Z Tranform of the sequence: $x(n)=n, \quad n=0,1,2,3,4,5 \Rightarrow X(z)=\sum\limits_{n=0}^{N-1}nz^{-n} $ I have searched everywhere I could, but in every single example there is a coefficient raised in $n$ which…
Adam
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How to perform Inverse Z transform

I'm trying to compute this Inverse Z Transform: $\displaystyle X(z) = \sin\left(\frac{1}{z}\right)$ Suppose that the sequences are right handed and one sided Any help would be appreciated.
Hernan
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To find Z-transform of given sequence

How to find the $z$-transform of $\left[a^{n}\sin\left(bn\right)\right]/n!$ where "!" denotes factorial of a number and b is constant??
rock321987
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How can I find the inverse z-transform of $\frac{1}{\left(z-\frac{1}{2}\right)^3}$?

I'm trying to find the inverse z-transform of $Y(z) = \frac{1}{\left(z-\frac{1}{2}\right)^3}$ but I just don't find how. I was trying to adapt the function so I could find it directly by using properties but it was useless. Btw it is my first…
Dajuvaja
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