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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Why the number of poles and zeros for a RHS signal in the Z domain is equal?

I can not understand the reason why the following sentence is true: If we have a Right-Hand signal(RHS) x(n), X(z), the Z-transform of x(n), has the same number of poles and zeros except at z = ...
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Conversion from laplace transform to z-transform [closed]

I would like to know if $$ \text {Z-Transform ( } G(s)H(s) \text{ )} = \text {Z-Transform (}G(s) \text{)} \text { Z-Transform (} H(s) \text{) } = G(z)H(z) $$ where G(s), H(s) are the Laplace ...
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Difference between DFT and Z-Transform

I have searched this question but couldn't find the answer in this network. I know this is very confusing question for DSP beginners. Both DFT and Z-transform work for Discrete signal. I have read ...
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Why do we care about the multiplicity of poles and zeros in rational Z-transforms?

In the DSP class I'm taking, a lot of the questions ask me to list the multiplicity of a pole or zero in a rational Z-transform. For example, the multiplicity of the zero at $z=1$ in :$\frac{(z-1)^2}{(...
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Digital filters and the Z-transform

Why is it that we Z-transform a difference equation to get a the transfer function of an digital filter? How come a digital filter is given in the Z-domain, and what is the Z-domain? And for that ...
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618 views

Understanding $\mathcal Z$-transforms and pole locations

I am trying to gain a better understanding of pole locations in the $z$-plane of a given discrete transfer function, $H(z)$. I think I have a pretty good understanding of how to use the $\mathcal Z$-...
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170 views

Obtaining the magnitude of the frequency response by plugging $e^{jω}$ into the z-domain transform function?

I am reading a text on discrete signal processing, which states that the frequency response of a signal can be obtained by plugging the value $e^{jω}$ into the z-domain transfer function $H(z)$. In ...
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468 views

Attempting to use the trapezoidal rule to form a difference equation representing a circuit

I have a differential equation that has been proven to be correct. The transfer function obtained by Laplace domain analysis and Matlab freqs match up and all is well. The problem is somewhere in ...
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14k views

Z-Transform of a^|n|

I am wanting to compute the Z-transform of $f(n) = a^{|n|}$ . 'a' is a positive constant. Looking at the transform table, I found that Z-transform for $a^n u(n)$ is available from the tables and is $...
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If I want to apply a filter to an Image should I use the IIR or FIR filters?

So I have discrete pixel values in the image and each row or column would make a signal. I would like to filter some of the rows or columns to remove high frequency components from them. Should I use ...
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Find output of digital filter given input and transfer function?

Hey guys so I have an input sequence that are real values that represent intensity of a column of an image. I also have the transfer function in the Z domain of a 2nd order high pass filter. I have ...
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How can I prove stability of a biquad filter with non-zero initial conditions

Ok, so the situation is that I have a DFII biquad with some filter coefficients: \begin{align} w[n] &= x[n] - a_1*w[n-1] - a_2*w[n-2]\\ y[n] &= b_0*w[n] + b_1*w[n-1] + b_2*w[n-2] \end{align}...
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Intuitive interpretation of Laplace transform

So I am getting to grasps with Fourier transforms. Intuitively now I definately understand what it does and will soon follow some classes on the mathematics (so the actual subject). But then I go on ...
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805 views

Calculating filter parameters from system response

In trying to answer another question, I got stuck applying what I thought would be a valid way to answer it: using the system function. Here's what I did: First, I put the question ...
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what is the frequency response?

I try to work out the simplest system, whose response is $H(z) = 1 + cz + c^2z^2 + c^3z^3 + \cdots = 1 / (1-cz)$ Now, Z-transform done quick (Fourier connection) and 4.5 Transfer Function, Poles and ...
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Where can I find a table of $z$-domain coefficients for Butterworth filters?

The primary source lists Butterworth polynomials in s-domain and provides a link to bilinear transform for digital implementation. But, who needs analog specification in our digital world? Why should ...
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How to derive stability of analogue and digital systems

I'm trying to find out why digital systems are stable iff poles oh their transfer function are inside the unit circle (or are there any others conditions?). I understand analogous systems are stable ...
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Why is a feedback loop not represented by the least order transfer function?

I have a feedback loop with transfer $L(z)= \frac{H(z)C(z)}{1+H(z)C(z)}$. $$H(z) = h\quad \text{and} \quad C(z) = \frac{K}{z-\alpha}.$$ If I manually calculate the transfer function, I get: $$L(z) =...
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Can I determine a system's $z$-domain transfer function from its pole-zero plot?

Is it possible to generate the z-domain transfer function from a pole-zero plot diagram?
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Is this a valid z-transform of $ \frac{1}{n^2}u[n] $?

I was looking over some DSP and came across the following signal: $x[n] = 1/n$. So I wondered whether it had a z-transform but I soon realized that it fails to meet two conditions described here: .....
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281 views

Find the frequency response of a system

I'm trying to find the frequency response $$H(\omega) = Y(\omega)/X(\omega)$$ for this system- the signal equations are given: $$y[n] = v[n - M] - g * v[n]$$ $$v[n] = x[n] + g * v[n - M]$$ I've tried ...
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Z-transform of a downsampler

In this paper or multirate filtering, the author establishes the following mathematical relationship. Let $y_D$ be the output of a downsampler such that $$y_D[n] = x[Mn]$$ where $M$ is the ...
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Filter order estimation

Assume some unknown but small and finite number of poles and zeros in the complex Z plane, all with complex conjugates, producing some response. Strictly from the absolute value of a set of equally ...
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777 views

Understanding the transfer function of an FIR filter

I'm currently studying FIR filter and am having trouble understand how the following equation works, and it's implication. $$ y[n] = h[n] * z^n = H(z) \cdot z^n $$ I don't really understand how this ...
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What is the $\mathcal Z$-transform of Bessel function $J_0(\alpha n)$ sequence

What is the $\mathcal Z$-transform of the sequence $J_0(\alpha n)$ for $n \in \mathbb{Z}$? The Fourier transform of zero$^{\rm th}$ order Bessel function $J_0(\alpha x)$ is known to be $\frac{2}{\...
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Finding the z-transform of $h[n] = a^n\cos(2\pi \frac{n}{F_s}f_0)$ for $n ≥ 0$ and zero for $n < 0$

So I'm trying to decide whether the cosine part is intended to be plugged in for $z$ or whether it is strictly part of $h[n]$. (the number a lies in the open unit disk) I mean I was pretty sure it ...
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How does the $\mathcal Z$-transform's “region of convergence” work?

I'm a novice in DSP and I have few doubts regarding the $\mathcal Z$-transform and its region of convergence (ROC). I know what a $\mathcal Z$-transform is. But I'm having trouble with understanding ...

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