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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Finding inverse $Z$ Transformation of a LTI system and switching of input output signal regarding to difference equation

I have 2 stuffs that are bothering me: I have the equation: $y[n]=8x[n]-2x[n-2]-x[n-4]$ When $x[n]$ input and $y[n]$ output. Now, the system is swapped, $x[n]$ output and $y[n]$ input The difference ...
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2nd order Z transform system [closed]

Related to this. I have been into exploring the world of digital control loop but I have encountered a very simple problem. The unity negative feedback transforms a system which delays a signal by 1 ...
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Laplace transform of this simple parallel RLC circuit? (For audio speaker simulation ...)

SPEAKER AS RLC CIRCUIT I read this article here which demonstrates a simulation of a speaker as a simple RLC circuit where the RLC components are in parallel: MY GOAL I am interested in creating a ...
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What is the effect of carrier frequency offset (CFO) on the zeros of the z-transform?

Suppose I have a discrete-time signal vector, for example, x(n)=[1,a1,a2,…,aN]. The signal is then transmitted by using the single carrier pulses, constituting a single-carrier communication over a ...
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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, ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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? ...
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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 ...