Questions tagged [poles-zeros]
The poles-zeros tag has no usage guidance.
138
questions
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15 views
Stability of $x(n) = A x(n-1)+b$
I am looking at the following system:
$x(n) = A x(n-1) + b$
where x and b are vectors and A is a matrix. How can I derive the stability and causality conditions for such a system using Z transform?
If ...
0
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1answer
21 views
ROC of Z transform Doesnt include a pole on the boundary?
I cannot figure out what is going on here. I have an example problem in my book that says the ROC of a certain function is $$ 0.5 < |z| < \infty$$
The function's denominator is $$ 1 - z^{-1} + 0....
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2answers
32 views
Region of the coefficients of a quadratic equation that cause the roots of it to be in the unit disk
From Simon Haykin's Adaptive Filter Theory: consider the characteristic equation is $1+π_1π§^{β1}+π_2π§^{β2}=0$, then for the roots to be inside the unit circle (i.e. in the unit disk), the ...
0
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1answer
34 views
Real impulse response
It will be great if someone can explain me what exactly means "real impulse response".
Further more , what is the effect of such a response on ROC (Laplace plane) and in particular if its ...
3
votes
2answers
179 views
Notch filter: differences between IIR and FIR filters
I'm trying to understand this great answer from Matt L. . It's said that "One advantage of IIR filters is that steep filters with high stopband attenuation can be realized with much fewer ...
0
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1answer
62 views
Pole locations of Butterworth filter
I am reading Proakis book "DSP using Matlab", 3rd edition.
I am reading chapter 8, section 8.3, p. 402, and I am confused regarding the equation of poles (roots of denominator of system ...
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0answers
31 views
Query regarding complex poles and zeros ??always exist as conjugate pairs?
Complex poles and zeros always exist in conjugate pairs?If yes,in which context?
https://www.informit.com/articles/article.aspx?p=32090&seqNum=9
The above link mentions this idea with eq 3.50
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0answers
33 views
Why does the filtered signal amplitude increase exponentially?
I am new to signal processing. I am having a problem applying a filter to a test signal. I am working with MatLab.
My test signal is a chirp up to Nyquist frequency and my filter is in zeros and poles ...
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49 views
How to water level deconvolve a noisy signal if i have a zeros and poles file?
Thanks for your time and help!
I am working with Apollo project passive seismic experiment (PSE) data, and I have a large set of seismic records (on digital counts) and the corresponding file of poles ...
0
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1answer
40 views
Plotting Frequency Response Magnitude and Phase for first order all pass filter
Having trouble plotting the frequency response characteristics for first order all pass filter. The Magnitude is expected to be constant across entire freq and Phase is expected to be only decreasing (...
0
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2answers
30 views
Apply Transfer Function in Continuous Domain in Matlab
I have the coefficients of a transfer function (i.e. numerator and denominator) in Laplace domain. How can I apply this to an input waveform using MATLAB script? I am looking for a function or piece ...
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22 views
Calculating Transfer function numerator and denominator from the rationalfit model
I have a frequency response data called 'AC_data' which is a vector of complex numbers (real and imaginary part) at different frequency points.
I have calculated a rationalfit model for the AC_data ...
2
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4answers
239 views
Single pole IIR filter, fixed point design
We want to do a fixed point implementation of the single pole IIR filter:
$y[n] = a\cdot x[n] + (1 - a)\cdot y[n-1] \quad ;\qquad 0<a<1$
What are the main design considerations to think about ?...
0
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2answers
64 views
Using ROC to find stability of system in specific example
I've started learning about finding the ROC from the transfer function, but I'm confused about an example.
$$H(Z) = \frac{2Z + 1}{Z^2 + Z - \frac{5}{16}}$$
I understand the poles lie at $z = \frac{-...
1
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1answer
83 views
How to match zero-pole diagrams to their frequency responses (Discrete Time)
I get confused when there are a lot of zeros/poles in the zero-pole diagram and I find difficulty understanding their frequency response.
I know the following:
1. Complex conjugates cause double ...
1
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3answers
120 views
Is $\cos(\pi \sqrt n)u[n]$ stable?
I took a z transform and got a double pole at $z=1$, but I don't know if that's correct.
I'm lost because I don't know if $\cos(\theta)$ converges or diverges or what that means for $h[n]$ being ...
0
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3answers
144 views
Necessary Conditions for stability in z domain?
What are the necessary(must) conditions for stability in z domain?
I am sure about one(ROC must include unit circle)
Is there any other such condition which states that there shouldn't be any poles in ...
0
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1answer
47 views
Finding poles of an abstract transfer function
When finding the poles of something like the following transfer function, would I be able to write $z=\sqrt[L]{\mu}$ since square roots aren't technically defined on the complex plane?
$$Y(z) = \frac{...
0
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1answer
49 views
What is difference between repeated poles and distinct poles? [duplicate]
What is difference between repeated poles and distinct poles?
As far as i am able to understand is that repeated poles are those that have same value of both x and y coordinates while distinct poles ...
0
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1answer
51 views
ROC vs stability in z domain?
I have read in some dsp texts that when ROC includes unit circle,system is stable
But i am bit confused in difference between stability and marginal stability depending Upon ROC
Especially i am ...
2
votes
1answer
1k views
Who first understood the importance of poles?
Who first understood (or at least published papers on) the importance of poles in understanding transfer functions in the frequency domain?
If I had to guess, I'd suggest Nyquist or Bode but I know ...
3
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1answer
72 views
ROC of the function in the problem 9.14 of Oppenheim's Signals and Systems textbook
I have solved the problem 9.14 in Oppenheim's Signals and Systems textbook, but my solution and the one in Slader is different. Problem is given above. And Slader solution is here.
I have also ...
1
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1answer
68 views
Causality of z-transform $a^nu[n+1]$
To preface, this is not a homework related question but purely for self-study purposes.
I'm try to do the analyse of z-transform of $a^nu[n+1]$. It is clearly a non-causal signal, I try to explain it ...
4
votes
1answer
271 views
Difference between repeated poles and distinct poles?
An important concept in dsp is marginal stability where we often see the term" repeated roots " or "repeated poles "?
What are they?
Does the term repeated means that two or more poles occur at ...
2
votes
1answer
216 views
get poles and zeros of frequency response
I am working on a python based LTSPICE project.
I would like to get poles and zeros of AC simulation data. Is there a way to get them under use of the magnitude and phase out of the frequency ...
2
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1answer
267 views
Lead compensator vs lag compensator?
I already know that lag compensator acts like PI controller and improves steady state and lead compensator acts like PD controller improves transient state but how they achieve their goal? Despite ...
1
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1answer
524 views
Pole Zero plot given a Transfer function
I've been looking at how to plot zeros/poles based on a transfer function. I found a couple of Tutorials online.
In the first youtube tutorial, the author brilliantly explains how to plot the zeros/...
0
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1answer
141 views
Are MATLAB function zp2tf() and tf2zp() are complementary or not?
I was under impression that given, pole, zero and gain the transfer function (filter coefficients b and a) is fixed. Therefore, ...
0
votes
1answer
59 views
Find the length of the impulse response of a Linear Phase Type 4 FIR filter
The length should be found such that the group delay is minimum
It is given that the impulse response is real. One zero of the Transfer function is at $0.6e^{j\frac{\pi}{4}}$, and another one is at -...
1
vote
1answer
785 views
How to realize Poles and zeros at infinity??especially through transfer function?
I have a question regarding the poles and zeros at infinity
I often read here in DSP SE and also in some textbooks about poles and zeros at infinity
This question also answers somehow (but not in ...
1
vote
1answer
1k views
Effect of origin poles on stability?
What will be stability if we have only one single pole at origin in s domain??
and what will be the case for multiple poles at origin in s domain?
0
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1answer
76 views
How can the Poles of the Root Locus be negative?
My understanding of drawing a root locus diagram is that stability requires all roots of the characteristic polynomial of the open loop transfer function to lie in the negative real part of the plane. ...
0
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1answer
680 views
Poles and zeros map, High pass filter
Given the following poles and zeros map I have to identify qualitatively, which filter type is represented (Low-Pass, High-Pass, ...). In the solution it says, that this is a high pass filter.
...
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0answers
48 views
Powers of $z$ in a discrete transfer function
I have been working with discrete-time systems and I am not yet able to understand the reason behind using powers of $z^{-1}$ in transfer functions.
I get that $z^{-1}$ means a delay, but when we ...
0
votes
1answer
435 views
pole/zero plot & impulse response
in a mock exam of dsp was asked this question, and even in knowing how to compute DFT's of the plot, I wondered if there was a fast way of pairing these plots to their respective impulse response?
...
0
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1answer
59 views
How to design a a filter and how to determine the poles and zeros on the basis of following informations?
A sinusoidal signal of 300Hz frequency,3V amplitude is contaminated with line frequency (50Hz,1V). Design a digital filter including poles and zeros to remove the interference component. Consider the ...
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0answers
91 views
Where to start in the design of my filter to remove 50 Hz
pick any 3 random files from this database, : https://physionet.org/pn3/ecgiddb/
They are subject to 50 Hz powerline interference.
We wish to convert from time domain to frequency domain and remove ...
0
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2answers
762 views
Z transform - Inverse System function - Why number of poles and zeros myst be equal?
I know that if a system is causal then the system function H(z) must have :
a) a ROC that spans from the exterior of the most distant pole and
b) the number of zeros must not be greater than the ...
0
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0answers
35 views
The range of r can be r<1 and r>1
I have to find the range of r which makes H(z) stable. There is no restriction of left sided or right sided.
Then, both r<1 (z>r) and r > 1 can be the answer?
2
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1answer
26 views
Plane Settings of the Matched $z$-transform Method
I've come across that the matched $z$-transform maps poles of the $s$-plane design to locations in the $z$-plane. My question is, what is the $s$-plane and what does this mean? I'm aware that the ...
2
votes
1answer
847 views
Nyquist Plot for transfer functions with poles at the origin
I'm learning Nyquist plots and something has been seriously bugging me when treating poles or zeros in the origin. Nyquist plots obtains information based on the argument principle which states
"If f(...
5
votes
2answers
562 views
Pole-zeros of a real-valued causal FIR system
Could someone please help me with the following question?
Below is the magnitude response of a real-valued causal linear phase FIR system of order N = 6. Determine the location of poles and zeros.
I ...
5
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2answers
703 views
How to determine if a filter is bandpass/stopband from its pole-zero diagram in z-domain
How can we determine if a filter is bandpass or stopband, just by looking at its pole-zero diagram in z-domain?
For exmaple, if we have a system with third-order pole at the origin and a zero on the ...
2
votes
1answer
368 views
Phase contribution of complex poles
I am struggling with understanding the phase contribution of each individual pole. Let's say we have a system (minimum-phase system if it makes a difference) and it has poles located at:
and
What is ...
0
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0answers
105 views
Poles and zeros representation in s-plane
We have a filter (or a system) that has two poles at $f_{p1} = f_{p2} = 20$ GHz and one zero at $f_{z1} = 15$ GHz. Let's assume the gain is $K = 1$. Then how do you mark these poles and zero in the ...
0
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2answers
267 views
Transfer function from poles and zeros
If we know that a filter (or a system) has two poles at 20 GHz and one zero at 15 GHz, then how do you write the transfer function $H(s)$ for such a system?
I am wondering why sometimes the poles and ...
2
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1answer
68 views
Hidden zero in system equation $H(z)$
An FIR linear phase filter has unit sample response $h[n]$ that is real with $h[n]=0$ for $n < 0$ and $n > 7$. If $h[0]=1$ and the system function has a zero at $z=0.4e^{j\pi/3}$ and a zero at $...
1
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1answer
53 views
Does the system function H(z) for a filter always have symmetry above and below the real x-axis?
When I look at the Pole/Zero diagrams in the DSP books it appears that whatever
pole or zero is above the real x-axis from:
$$\omega=0 \rightarrow \pi$$
is always reflected as a mirror image ...
0
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1answer
681 views
Is the inverse of a causal system also causal?
If I have a causal system H(z) and I find the inverse of this system:
$$
G(z) = \frac{1}{H(z)}
$$
Is G(z) also causal?
0
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1answer
591 views
Get the discrete-time poles and zeros from continuous-time poles and zeros
How do you implement the following function:
$$[Z^d, P^d, K^d] = \text{fcn} \,(Z^c, P^c, K^c),$$
where $Z^c = [z^c_m, ..., z^c_1]$, $P^c = [p^c_m, ..., p^c_1]$, and $K^c$ are zeros, poles, and gain ...
