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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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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40 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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122 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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184 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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45 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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29 views

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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137 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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53 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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51 views

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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99 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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39 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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55 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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70 views

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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32 views

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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38 views

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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1answer
75 views

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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87 views

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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43 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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210 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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77 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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44 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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217 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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30 views

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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248 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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565 views

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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53 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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145 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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207 views

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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51 views

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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132 views

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 ...
2
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1answer
128 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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234 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 ...
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238 views

How can I prove stability of a biquad filter with non-zero initial conditions

Ok, so the situation is that I have a DFII biquad with some filter coefficients: $w[n] = x[n] - a_1*w[n-1] - a_2*w[n-2]$ $y[n] = b_0*w[n] + b_1*w[n-1] + b_2*w[n-2]$ While the filter is ...
2
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1answer
200 views

Intuitive interpretation of Laplace transform

So I am getting to grasps with Fourier transforms. Intuitively now I definately understand what it does and will soon follow some classes on the mathematics (so the actual subject). But then I go on ...
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150 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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115 views

what is the frequency response?

I try to work out the simplest system, whose response is $H(z) = 1 + cz + c^2z^2 + c^3z^3 + \cdots = 1 / (1-cz)$ Now, Z-transform done quick (Fourier connection) and 4.5 Transfer Function, Poles and ...
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819 views

Where can I find a table of $z$-domain coefficients for Butterworth filters?

The primary source lists Butterworth polynomials in s-domain and provides a link to bilinear transform for digital implementation. But, who needs analog specification in our digital world? Why should ...
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1answer
365 views

How to derive stability of analogue and digital systems

I'm trying to find out why digital systems are stable iff poles oh their transfer function are inside the unit circle (or are there any others conditions?). I understand analogous systems are stable ...
3
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105 views

Why is a feedback loop not represented by the least order transfer function?

I have a feedback loop with transfer $L(z)= \frac{H(z)C(z)}{1+H(Z)C(z)}$. $H(z) = h$ and $C(z) = \frac{K}{z-\alpha}$. If I manually calculate the transfer function, I get: $L(z) = ...
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140 views

Can I determine a system's $z$-domain transfer function from its pole-zero plot?

Is it possible to generate the z-domain transfer function from a pole-zero plot diagram?
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88 views

Is this a valid z-transform of $ \frac{1}{n^2}u[n] $?

I was looking over some DSP and came across the following signal: $x[n] = 1/n$. So I wondered whether it had a z-transform but I soon realized that it fails to meet two conditions described here: ...
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184 views

Find the frequency response of a system

I'm trying to find the frequency response $$H(\omega) = Y(\omega)/X(\omega)$$ for this system- the signal equations are given: $$y[n] = v[n - M] - g * v[n]$$ $$v[n] = x[n] + g * v[n - M]$$ I've tried ...
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739 views

Z-transform of a downsampler

In this paper or multirate filtering, the author establishes the following mathematical relationship. Let $y_D$ be the output of a downsampler such that $$y_D[n] = x[Mn]$$ where $M$ is the ...
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172 views

Filter order estimation

Assume some unknown but small and finite number of poles and zeros in the complex Z plane, all with complex conjugates, producing some response. Strictly from the absolute value of a set of equally ...
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381 views

Understanding the transfer function of an FIR filter

I'm currently studying FIR filter and am having trouble understand how the following equation works, and it's implication. $$ y[n] = h[n] * z^n = H(z) \cdot z^n $$ I don't really understand how this ...
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264 views

What is the Z-transform of Bessel function $J_0(\alpha n)$ sequence

What is the Z-transform of the sequence $J_0(\alpha n)$ for $n \in \mathbb{Z}$? The Fourier transform of zeroth order Bessel function $J_0(\alpha x)$ is known to be $\frac{2}{\sqrt{\alpha^2 - ...
8
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1answer
342 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 ...
7
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1answer
4k views

How does the Z transform's “region of convergence” work?

I'm a novice in DSP and I have few doubts regarding the Z transform and its region of convergence (ROC). I know what a Z transform is. But I'm having trouble with understanding the ROC. First of all ...