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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Z Transform problem

I have a class exercise of an inverse Z transform and I have some trouble. I will render an example to make my point. Let's asume the Z transform pairs: $$a^n \cdot u[n] \Leftrightarrow ...
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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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z-transform for baseline correction for an ERP signal for performing FFT

For a time frequency analysis of an Event related potential (ERP) signal I want to perform Baseline correction. For my signal power is too high for the regular subtraction method. Can I use ...
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45 views

just getting started in Signal Processing - easy question

I am reading Cycle Analytics for Traders by John Ehlers and need help. in the first section "Transfer Response" he refers to: so if I had $4$ prices say $8+8+8+8$ then average would be $8$ and ...
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36 views

How to compute magnitude and phase response from transfer function in Z-domain?

I have a transfer function $$H(z)=\frac{1+1.2z^{-1}+0.8z^{z^-2}}{1-0.9z^{-1}}$$ from which I'm supposed to sketch the magnitude and phase response. I know that you can transform $z=e^{jw}$ to get the ...
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31 views

Can someone explain complex mapping as appears in Ogata's textbook

Refer to diagram above, in Ogata's text on discrete time control, he showed that you can map a curve in the S plane, namely curve 1,2,3,4,5 onto a circle in the Z plane through the complex mapping ...
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34 views

How to prove this theorem about the Z transform and final value theorem?

Claim: If $\lim_{k\rightarrow\infty} x[k]$ exists and is finite then $X(z)$, the Z-transform of $x[k]$, has no poles in the region $|z|>1$ and at most 1 pole at $z = 1$. Attempt: ...
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How to intuitively understand the state space formulation of discrete time system?

The SS formulation of DT system is given by $$x[(k+1)T] = Ax(kT) + Bu(kT)$$ $$y(kT) = Cx(kT) + Du(kT)$$ Note: T is the sampling period and often omited Can someone explain to me why the state ...
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42 views

Claim: Given sampling time T, the hold operator is approximated at low frequency by a time delay of T/2

Can someone verify this statement? The hold operator is assumed to be a zero order hold Then the laplace transform of this hold operator has a well known form $(1-e^{-sT})/s$ Let w approach 0, we ...
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74 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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62 views

Eigenfunction of LTI causal system Z-transform

I am studying for my DSP final and I came across this question from the Oppenhiem and Schafer book 3rd edition. The question says 3.18 A casual LTI system has the system function ...
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2-sided Regions of convergence for Z transforms

Given a z transform with one pole can you have a 2 sided Region of convergence or does 1 pole limit it to being only left or right sided? I know when you have two poles the 2 sided scenario is when a ...
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25 views

Conceptual queston on Z transforms and time series model (Part2)

I am learning the fundamentals of signal processing and time series models and I am having a hard time to follow due to lack of basics related to $z$ transforms and autoregressive model. I am facing ...
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61 views

Conceptual queston on Z transforms and time series model (Part1)

I am few questions from the following papers: ...
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115 views

How to show that y[n] = x[n] * h[n] turns into the Y(z) = X(z).H(z)?

I'm trying to show that $y[n]=x[n]*h[n]$ turns into $Y(z) = X(z)H(z)$ in Z-domain by first applying convolution then by taking the inverse Z-transform of the $Y(z)$, stating that it's the same ...
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28 views

Magnitude and Phasor Response of Direct Form 1

i want to draw the magnitude and phasor response of the given equation $H(Z) = (0.0605 +0.121z^{-1} + 0.0605z^{-2})/(1-1.194z^{-1} + 0.436z^{-2})$ I need Matlab code and also explain that how will i ...
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DSP interview question: use of the identity in development of a significant transform

I'm preparing interview and found this question. But I don't really understand what is the question. Does it ask about Fourier transform or Z transform? How the simple identity $$xy=\frac{1}{2}x^2 ...
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91 views

Difference Equation & Impulse Response of IIR filter - deconvolution

What i want to do is to design an IIR-filter that cancels the "echo", such that im only left with the delta[n]. To do so i ofcourse make an IIR-filter, where u take the z-trans of the impulse ...
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49 views

Pole/Zero existence at infinity

How can poles and zeros exist at infinity?Can anybody explain using a system function?
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126 views

Study Signal Processing

I'd Like to ask two questions : What is the difference between studying Signal processing (both Deterministic and statistical) in Department of Electrical Engineering versus Department of Mathematics ...
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388 views

Real and Imaginary Frequency Responses of a single complex pole

I'm filtering a real signal with a single complex pole with a complex coefficient (a_re [real part] and a_im [imaginary part]), I also have a gain coefficient but I'm gonna leave it out for the sake ...
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56 views

Z Transform - ROC values

I was reading a DSP book where they had a problem on Z Transform. Determine the z-transform and ROC for signal $\displaystyle x(n) = a^nu(n)$? The solution states that $$ \displaystyle X(z) = ...
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Z-Transform amplitude

I've tried to compare the Bode plot of a discrete-time system with a manually computed Z-transform in Matlab like this: ...
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344 views

Are Z-transform time shifting and differentiation properties always compatible?

I'm currently studying the Z-transform, and I'm having issues in understanding the time shift and differentiation properties, to be precise: calculating a Z-transform explicitly, and obtaining it by ...
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59 views

Deriving finite impulse response for polylogarithm

As a part of my research i have to use the following z-transform in matlab 'filter' function so as to derive the convoluted signal from the original one. $$\frac{1}{{\rm Li}_{k}(z^{-1}e^{-b})}$$ ...
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Confusion regarding bilinear transform

I was reading my book where the z-transform of a signal is derived to be ${1-e^{-2bT}z^{-1}}$ . Then it goes on to say that by applying the bilinear transform we can get ...
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183 views

Inverse Chirp Z Transform

I am working to understand and use the Chirp Z-Transform. I want to use the algorithm for simple signal processing on data sets that are not a power of two. I need to be able to inverse transform as ...
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51 views

Z-transform and binomial series

I am reading a paper on frequency warping and I need to do a little manipulation of the Z-transform. Can somebody help me on how can I go about deriving equations $(3)$ and $(4)$ from equations $(1)$ ...
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61 views

Does the ROC (Z-Transform) always start/end from/in a pole?

Can I assume that the R.O.C. from a Z-Transform will always start from or end in a pole or 0/infinity? Using an example: $$H(z)=\frac{(z+1)(z-1)(z+j)(z-j)}{z^4}\space,\space\space j=\sqrt{(-1)}$$ ...
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Z transform convergence

From the definition I know: $$|\sum_{n=-\infty}^{+\infty}x[n] \cdot z^{-n}| < \infty\space\space\space(1)$$ Is there any sequence of x[n] which can not be written as $$x[n] = y[n] \cdot ...
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Is it possible to calculate a z-transform for a filter calculated with Parks-McClellan?

I would like to know whether this can be done and if then how would this feat be acomplished in Matlab given a filter calculated with Remez? h = remez(...); If ...
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Connection with system analysis and laplace&Z transform

Laplace&Z transform is just frequency analysis of a system with a multiplication of decaying exponential. We analyse frequency with varying Laplace Exponential, which can be seen in the formula ...
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Generating a time series given a transfer function

I'm trying to work my way through a paper I found online, titled "Three Models of Wind-Gust Disturbances for the Analysis of Antenna Pointing Accuracy" by W. Gawronski, 2002. ...
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IIR filter SOS and Direct Forms doubt

I have below doubts, so confusing! As I don't want to assume from what I read, I am asking for help here! Are Second Order Sections another name for biQuads ? If I have 2 single pole transfer ...
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48 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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356 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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191 views

Minimum phase systems with pole at infinity

If a system is given by a transfer function in the z domain that has all poles and zeros inside the unit circle except for a factor of $z^{-1}$ in the denominator (pole at infinity), can it still be ...
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49 views

Region of Convergence for pole at z=-1 ?

I am caught up in a following question: I have a mixed (causal + anti-causal) input to a system whose output is causal, with system having transfer function with pole at z=-1 and zero at z=1. What is ...
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595 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 ...
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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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663 views

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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59 views

Why do we care about the multiplicity of poles and zeros in rational Z-transforms?

In the DSP class I'm taking, a lot of the questions ask me to list the multiplicity of a pole or zero in a rational Z-transform. For example, the multiplicity of the zero at $z=1$ in ...
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190 views

Digital filters and the Z-transform

Why is it that we Z-transform a difference equation to get a the transfer function of an digital filter? How come a digital filter is given in the Z-domain, and what is the Z-domain? And for that ...
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Understanding Z-Transforms and Pole Locations

I am trying to gain a better understanding of pole locations in the Z-plane of a given discrete transfer function, $H(z)$. I think I have a pretty good understanding of how to use the Z-transforms ...
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Obtaining the magnitude of the frequency response by plugging $e^{jω}$ into the z-domain transform function?

I am reading a text on discrete signal processing, which states that the frequency response of a signal can be obtained by plugging the value $e^{jω}$ into the z-domain transfer function $H(z)$. In ...
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Attempting to use the trapezoidal rule to form a difference equation representing a circuit

I have a differential equation that has been proven to be correct. The transfer function obtained by Laplace domain analysis and Matlab freqs match up and all is well. The problem is somewhere in ...
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161 views

Z-Transform of a^|n|

I am wanting to compute the Z-transform of $f(n) = a^{|n|}$ . 'a' is a positive constant. Looking at the transform table, I found that Z-transform for $a^n u(n)$ is available from the tables and is ...
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65 views

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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310 views

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 ...