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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2answers
6k views

What is the difference between natural response and zero input response?

I am new to DSP and was going through different responses of a system subjected to an input. My understanding of zero input response is: it is the response/output of the system when the input signal ...
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1answer
3k views

Do Causal Discrete-time systems have proper transfer functions?

In the case of continuous-time systems, if the system is causal, its Laplace transfer function is strictly proper (the degree of the numerator is less than the degree of the denominator). Is this ...
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2answers
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How/why are the $\mathcal Z$-transform and unit delays related?

The $\mathcal Z$-transform uses the same notation as the unit delay $z^{-1}$, but in $\mathcal Z$-transform $z$ is a complex number. What's the relation between the $\mathcal Z$-transform and the ...
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2answers
643 views

z-Transform Methods: Definition vs. Integration Rule

The definition of the z-transform is defined as $z = e^{sT}$ where "s" is complex frequency for continuous-time systems and "T" is the sample period. Why are rules such as the forward rectangular ...
5
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1answer
160 views

$\mathcal{Z}$-transform of $\frac{1}{n^2}$

This is a Question asked in IISC ( Indian Institute of Science,Bangalore,India) interview for MS admission. What is the $\mathcal{Z}$-transform of $\dfrac 1{n^2}$ ?
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1answer
117 views

Bilateral $\mathcal Z$-transform of exponential

We all know that $a^nu(n)$ has unilateral $\mathcal Z$-transform. But what is the $\mathcal Z$-transform of $a^n$? (bilateral) When i tried to solve, i got answer as 'zero'. But bilateral Laplace ...
4
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1answer
11k views

Identifying the magnitude and impulse response from pole zero plot quickly

I have an exam next week and it's verty certain that a task of this kind will be there. Are there some good tips how to match the right pole zero plot to the right responses? No proof is needed in ...
5
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1answer
323 views

Understanding the $\mathcal Z$-transform

I was studying $\mathcal Z$-transforms and found pretty good material on the topic, though I feel I do not have a proper understanding of the concept. Could someone help me clarify this? I know that ...
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2answers
3k views

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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1answer
1k views

Minimum number of Poles and zero of transfer function H(z)?

Suppose $G(z)=H(z)(1-\frac{1}{2}z^{-1})$ now in question its saying ROC of G(Z) is entire Z plane except Z=0,so here we need not to add anything because G(Z) already a right sided signal with ROC ...
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1answer
2k views

Inverse z transform - contour integration

Here is my task: Find inverse z transform of $X(z)=\frac{1}{2-3z}$, if $|z|>\frac{2}{3}$ I need to find it using definition formula, $x(n)=\frac{1}{2\pi j}\oint_{C}^{ } X(z)z^{n-1}dz$. How can I ...
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1answer
108 views

How do I find the difference equation from a transfer function?

Most of the resources I found online go the other way. If I have the transfer function $H(z) = 1 - cos(\theta) \cdot z^{-1} + z^{-2} $ how do I get the difference equation from it so that I can ...
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3answers
289 views

Can I study continuous time Fourier Transform and treat the rest as special cases

Say I learned the theoretical result of continuous time Fourier transform. And I want to extends some results(say "convolution rule") to Lapace transform, Z transform, DTFT, DFT, Fourier sequence ...
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3answers
110 views

Inverse z-transform. Where is mistake?

I've already wrote about that trouble (link here), but I don't understand where I've made a mistake. Full description of the task is as follows: Z-transform of sequence {x(k)} describe by the ...
2
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1answer
4k views

How to implement a filter in matlab

I want to implement the 'filter' function in matlab but I just can't seem to replicate the results I get when using the matlab function. My understanding of the matlab function is that it takes 3 ...
2
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3answers
437 views

Finding Fourier transform of a discrete signal from its Z-transform

Is it possible to find the Fourier transform of a discrete signal if you know its $\mathcal{Z}$-transform of?
2
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1answer
104 views

Transient response of system with single pole $0 \le p < 1$

$G(z) = \frac{1-p}{z-p}$ If the value of p satisfies $ 0 \leq p < 1$ there are no oscillations in the transient response. Question: Why is that $\uparrow$ true? I know roughly what a ...
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1answer
157 views

$\mathcal Z$-transform ROC

Let's say I have a $\mathcal Z$-transform that represents some transfer function and its has some ROC. My question is how do I know if this system is causal? I know that if the ROC contains the ...
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1answer
2k views

use chirp z transform for spectral resolution

let us suppose that we some signal $x(t)$,which consist of sinusoidal components and white noise,i would like to know how to use chirp z transform for improving spectral resolution?i found this ...
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2answers
49 views

Squared magnitude of System Function H(z)

If: $$ |\alpha|^2 = \alpha \alpha^* $$ Then, why does: $$ |H(z)|^2 = H(z) H(z^{-1}) $$ instead of: $$ |H(z)|^2 = H(z) H^*(z) $$
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1answer
743 views

Converting poles/zeros to differential/difference equation solutions

Does anyone have a reference handy on how to convert poles and zeros of a system to differential/difference equations. Here is a quick draft of math, but I am not sure if it's at all correct. First, ...
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1answer
64 views

Z-transform of x[a -n]…where a is int

i try to calculate the $\mathcal z$-transform of $x[a-n]$ (where $n$ is my variable) i can't find any transform. the best suited transform is $x[-n] \longleftrightarrow X(z^{-1})$ i took the sum ...
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2answers
111 views

Trouble with inverse Z-transform and calculating of samples

I have a little problem. I have to solve this task but I can't. Z-transform of sequence $\{x(k)\}$ describe by the formula: $$X(z) = \frac{2.5 -3.15z^{-1} + 1.2 z^{-2}}{1-2.3z^{-1} + 1.2z^{-2}...
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1answer
731 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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0answers
178 views

z-transform of $2^k$

It seems that you can decompose it as such: $f(n) = a^n u(n) + a^{-n} u(-n-1)$ But I already have issue here, is it basically saying that $ u(n) + u(-n-1) = 1$? this is the plot of u(n) and u(-...
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1answer
106 views

Why Z-transform is considered as separate transform?

The mathematical formula of the Laplace and Z transforms are same with just one difference. I.e. in the first we use $t$ for continuous-time signal and in the latter uses $n$ for discrete-time signal....
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1answer
67 views

Taking the inverse $\mathcal Z$- transform with a summation in the denominator

I'm learning about z-transforms, and was going through some practice problems and I've been stuck on this one for a little bit. I'm trying to take the inverse z-transform of the following: $$\frac{1}{\...