# 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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### How do I represent any signal in the form x[n]u[n] and x[n]u[-n-1]?

For eg-: If I have the signal x[n]={1,a,a²...}I can represent it as a^n * u[n]. Similarly if I havethe sequence as x[-1]=-a^-1 x[-2]=-a^-2 Then I can represent it as x[n]=-a^n*u[-n-1].
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### DSP: newbie not understanding z transform/complex sinusoidal frequency and phase

Im reading Will Pirkles Designing audio effect plugins book and I'm not sure if I'm understanding the z transform correctly. I got up to differential equations in college, but haven't done math in ...
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### Polar Fourier Transform and its similarity to the Z-Transform

The DFT is given by $X_{\mathcal{F}}(k) = \sum_{n=0}^{N-1} x_n e^{-j 2 \pi k n / N}$ Knowing that complex numbers can also be represented using a polar form $A \angle\theta$, I was looking for a ...
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### Having trouble interpreting z-transform description of a predictor from a codec paper

I've been looking at the opus paper (https://arxiv.org/pdf/1602.04845.pdf); in particular, in section 4.1, they describe the predictor for the current band energy based on energy from both the current ...
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### K-Path sampling overall transfer function

I'm trying to derive the overall Z-transform for the K-path sampling system shown below. I numbered some of the equations that I'll reference. I don't think I understand going from equation 3 to ...
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### Digtial FIR Impulse response & transfer function

I am currently working the figure through below. as it is an FIR Filter i have worked out using convolution that the output is 4,2,4,6,0,0. i am trying to obtain the 'z' domain transfer function of ...
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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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### 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 ...
According to this question and answer the following system cannot be adequately captured by a z-transform transfer function. $$y[n] = y[n-1] + F_{\psi}(y[n-1)) + F_{\phi}(x[n-1])$$ where $F_{\alpha}(z)... 2answers 240 views ### How can initial conditions be taken into account to calculate a system's terminal value using the final value theorem or some other technique I wish to calculate the Final Value of the following system given initial conditions not at rest, and assuming the X will not change from its initial condition value. The transfer function is$$H(z) = ... 1answer 58 views ### Discrete time Final Value Theorem applied to feedback system I wish to calculate the Final Value of systems in which a high pass filter of the output feeds back into the input. A simple example would be: where is a 1st order high pass filter with transfer ... 1answer 119 views ### Single-sided Z transform with difference equations and the system function I am working on this problem: Given an impulse response, find the system function, find the difference equation representation, find pole-zero plot, find output$y[n]$if the input is$x[n] = 0.25^n *...
I am trying to understand how the output behaves when the input and the system function do not have a common region of convergence (ROC) for an LSI system. Consider an LSI system with $x[n]$, $h[n]$, \$...