# 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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### MATLAB Implementation of Karplus Strong algorithm with filter function?

I want to implement following function: y = ksalgrithm(x, alpha, M, Nout) where x is the input vector with length ...
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### A question regarding z transform and its magnitude response

My teacher of signals and systems gave us a review problem as following: given a DT rightsided LTI system with transfer function $$\frac{1-a^*z}{z-a}, \left | a \right |<1$$ show that the system'...
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### Deriving Frequency Response for 2-pole Zero-Delay Feedback State Variable Filter

I have an existing zero-delay feedback (ZDF) 2-pole state variable filter implementation (along the lines of the theory presented in VA Filter Design by V. Zavalishin), and I wish to determine the ...
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### Determining the final value of the output of a discrete system

I'm going through an exam question where I've been told that the samples $f(kT)$ of the following function \begin{equation}{F\left(z\right)=\frac{1}{1-0.819z^{-1}}} \end{equation} are applied to a ...
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### What is the rule for manipulating the boundaries of a summation?

When working with DTFTs or $\mathcal Z$-transforms, we sometime get summations that do not go from $n=0$ to $+\infty$. For example, suppose we have the sequence $x(n) = -\alpha^n u(-n-1)$. To find ...
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### ROC of this LTI system given $x[n]$ and $y[n]$

So I have a system with the following inputs and outputs: \begin{align} x[n]&=\left( \frac12 \right)^{n}u[n] + 2^{n}u[-n-1]\\ y[n]&=6\left( \frac12 \right)^{n}u[n] - 6\left( \frac34 \right)^{...
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### Find the $\mathcal Z$-transform of this function?

I need to find the $\mathcal Z$-transform of $x(n)=a^{-n} u(n)$. Assume, $a$ is a positive constant , but the power of $a$ is negative. Looking at the transform table, I found that $\mathcal Z$-...
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### Finding the minimum phase h[n] and its Z transform

Hello, this is one of my homework questions and i have already solved the first question but im having trouble gettin a relation that helps me solve the second one. From the question i understand that ...
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### Simplify equation of single pole IIR transfer function

Example - Consider the causal stable IIR transfer function $$H(z)=\frac{K}{1-\alpha z^{-1}}, \quad 0 < \lvert \alpha\rvert 1$$ where $K$ and $\alpha$ are real constants Its square-...
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### Control systems and convolution

I think i am not understanding the concept of convolution well. Lets say we are given a system impulse response in the S-domain, and we have implemented a controller $G_c(s)$ that will adjust the ...
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### Bilinear Transformation Comparison

If I have transfer function coefficients, I can analyze the transfer function in the s-plane and/or the z-plane. If I wanted to demonstrate that the z-plane and s-plane responses are equivalent: ...
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### Does $H(-z)$ produce aliasing? [closed]

Given $H(z)$ is the z-transform of a signal, I know that $H(-z)$ results in shifting of frequencies in DTFT by $\pi$ or $-\pi$. Does it produce aliasing ? How ?
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### Inverse $z$-transform of a transfer function in MATLAB

I have designed a Butterworth highpass filter (HPF) of 4th order with cutoff frequency high enough to give a gain of $3$ at high frequencies. I want to find the inverse $z$-transform using MATLAB. <...
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### Is Z-transform of $\sin(\omega_0n)$ same as that of $\sin(\omega_0n)u[n]$

The Z-transform tables only mention the transform of $\sin(\omega_0n)u[n]$, e.g. #21 at this link: https://en.wikipedia.org/wiki/Z-transform#Table_of_common_Z-transform_pairs But how can I find of Z-...
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### Understanding the $\mathcal Z$-transform

I was studying $\mathcal Z$-transforms and found pretty good material on the topic, though I feel I do not have a proper understanding of the concept. Could someone help me clarify this? I know that ...
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### For a discrete LTI system, does “bounded memory” imply “rational transfer function?”

Every LTI system with a $\mathcal Z$-domain transfer function that is a rational function - aka a quotient of two polynomials in $z$ - can be implemented using a bounded amount of memory. Is the ...
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### $\mathcal{Z}$-transform of $\frac{1}{n^2}$

This is a Question asked in IISC ( Indian Institute of Science,Bangalore,India) interview for MS admission. What is the $\mathcal{Z}$-transform of $\dfrac 1{n^2}$ ?
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### Inverse $\mathcal Z$-transform problem

$B(z)+B(-z) = 2c$, explain the structure of $b[n]$ and find the constraint of its length given that $c$ cannot be $0$. This is a homework problem. "Explain the structure" means that $b[n]$ is zero ...
### $\mathcal Z$-transform, ROC of a system from dividing to others
TRUE / FALSE Given three systems with rational $\mathcal Z$-transform. Systems A and B are not stable with $\mathcal Z$-transform $H(z)$, $G(z)$ respectively. A and B have no common poles. System's C ...
### How/why are the $\mathcal Z$-transform and unit delays related?
The $\mathcal Z$-transform uses the same notation as the unit delay $z^{-1}$, but in $\mathcal Z$-transform $z$ is a complex number. What's the relation between the $\mathcal Z$-transform and the ...