# 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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### 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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### 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 ...