# 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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### Trivial and non-trivial zeros

I am new to DSP, and I'm self studying. Could someone please explain to me what do we mean by trivial and non-trivial zeros?
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### solving recurrence relation with Z-transform (LTI and causal)

I just wanted to doublecheck answers for my sanity's sake (exam next week) problem statement recurrence relation, solve it $y[n+1]= 35 + y[n]*0.5$ according to my teacher it will be such that the ...
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### Design a filter which passes all frequencies except $\omega=\pm\frac{\pi}{2}$ and plot its pole-zero diagram

Also draw its normalized frequency response. What is the ROC? This has to be done in z-plane so there must be two poles at $+i$ and $-i$ since they cannot be included in region of convergence. Is my ...
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### Autocorrelation of a Shifted Sequence

Suppose I have a sequence $x[k]$ with $\mathcal{Z}$-transform $$X(z) = x_{0} + x_{1}z^{-1} + x_{2}z^{-2} + \ldots + x_{N-1}z^{N-1}$$ I know that for real-valued $x[k]$ the $\mathcal{Z}$-transform ...
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### How to transform a Fractional Order Laplace Transfer Function into a digital filter?

I'm working with loudspeaker impedance analysis. Electrical behavior of loudspeakers can be modeled with RLC networks. But real loudspeakers have components, that exhibit some non-linear and frequency ...
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### periodicity, minimum phase, maximum phase, interpretation

I have a finite linear difference equation $$y(n)=ax(n-1)+bx(n-2)+cx(n-3)+\ldots+fx(n-m)\text,$$ relating an input $x(n)$ to an output $y(n)$. If I assume periodicity of type $x(n-2)=x(n)$, the ...
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### LTI system phase response given $z$-transform
Assume I have a discrete random signal, $f(t)$ for which I want to calculate the laplace transform. How can I do it in matlab without using sym variables, for ...