# 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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### Filter H(z) manipulation frequency response changes

I'm trying to understand how altering the frequency response of a H(z) low pass filter, will visually alter it's frequency response plot. For example: by doing H(z^2), would the frequency response ...
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### understanding echo cancellation model

so, here is a very simple model. The CCDE is given, but I was trying to derive it on my own and now I am stuck. first of all, the reverse y[n] when goes through the delayed system, it turns to y[n-M]....
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### use contour integration to determine x(n) whose z transform is given

use contour integration to determine the sequence x(n) whose z transform is given by
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### Can we choose a sampling frequency to remove unwanted noise at a specific frequency?

I am studying for my exam in signal processing. In one of the old exam papers I am told to find a sampling frequency, which will remove 80 Hz noise. The filter the exam question is based around has an ...
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### Why not use the same “standard” exponentials for both continuous and discrete time

In continuous time the standard exponential signal is usually defined as $$e^{st}, \quad\text{with}\quad s = \sigma+j \omega$$ In discrete time the standard exponential signal is usually defined as ...
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### Simple Filter representation in Matlab

Suppose I have an IIR filter in the $z$-domain in the following form: $$H\left(z\right)=\frac{1}{1-0.2z^{-1}-0.1z^{-2}}$$ How do I represent this in MATLAB? I am pretty sure if I just listed the ...
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### Magnitude response of mirrored (with respect to unit circle) poles and zeros

I just want to check that my understanding about the following paragraph from Optical Filter Design and Analysis by Christi K. Madsen, Jian H. Zhao is correct: A filter’s magnitude response is equal ...
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### Squared magnitude of the Z-transform

I am basically new to the $z$-transform and there are some points regarding its square magnitude that I do not understand. Basically I do not understand how in slide 4 of PDF, they arrive at the ...
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### Uncountable Set of Poles?

It is easy to define an (ideal) LTI system that would have an infinite number of poles - for instance, if the transfer function is $$H(z)=\frac{1}{\cos(z)-1}$$ However, this would only define a ...