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Methods to determine stability of open-loop systems

Which methods can be used to analyze the stability of open-loop systems only, closed-loop systems only, and both of them? As far as I understand, you can determine the stability of open-loop and ...
Tim's user avatar
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Need help with deriving a recursive formula for a control system optimization integral

I need some help with a problem that appears in one of the exercises of "Introduction to Stochastic Control Theory" by Karl J. Åström: Chapter 5, page 141, problem 8. It is about deriving a ...
mattTheMathLearner's user avatar
1 vote
1 answer
78 views

Decay of the impulse response for poles contained in the unit circle

I've been struggling with the following exercise in Ljung's "System Identification: Theory for the User" (Problem 3G.1): Given a rational transfer function $G(z)$ such that its poles are all ...
LSK21's user avatar
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How to handle non-causality when decomposing a 4th order IIR filter into a parallel bank of second order filters?

What I am trying to do I am trying to code a Gaussian smoothing filter using the 4th order IIR filter described in Van Vliet's paper "Recursive Gaussian derivative filters". My code works ...
Omar Emara's user avatar
1 vote
2 answers
154 views

Poles and Zeros in Time Domain

I was looking at this forum: A question about the meaning of pole in time domain, and I still have some doubts about the time domain input that would lead to a pole or zero. Let's say I have this TF $$...
BambaMentality's user avatar
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1 answer
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Why do singularities on the imaginary axis affect the Fourier transform differently than the Laplace transform?

(Please note that I'm aware there are already several questions asking about the difference between the two transforms. However, none of them that I could find touch on this specific issue of the ...
Mikayla Eckel Cifrese's user avatar
1 vote
1 answer
59 views

What is the effect of carrier frequency offset (CFO) on the zeros of the z-transform?

Suppose I have a discrete-time signal vector, for example, x(n)=[1,a1,a2,…,aN]. The signal is then transmitted by using the single carrier pulses, constituting a single-carrier communication over a ...
tuner's user avatar
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How do zeros outside the unit circle affect the stability of a system?

I'm learning about poles and zeros of transfer functions in my signals class and we have just covered the effects of poles outside the unit circle on the pole-zero plot. Intuitively, it makes sense ...
marco's user avatar
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1 answer
252 views

What is damping ratio and natural frequency of z-domain with real negative pole and undifine region

As ilustrated in controlsystemsacademy shown relation between z-domain and s-damain poles by this image. with contour for natural frequency and damping ratio given by these equations. However there ...
M lab's user avatar
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What can be the pole zero diagram [closed]

Does the pole zero plot for $$H(z)=(1-z^{-1})^3(1+z^{-1})^3$$ have 6 poles at origin and 3 zeroes at 1? Just answer yes or no, not your homework question knowledge
Bitsaa's user avatar
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Bilinear transformation with a high sampling rate (chebyshev filter)

I'm trying to design a digital Chebyshev filter of order 2. This gives the general transfer function If I transform this and simplify I get If I then expand the denominator and then normalize so ...
Johannes's user avatar
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Why a differentiator is unstable from pole zeros view point?

A differentiator with frequency response $j2 \pi f$ is unstable because as frequency increases its response becomes out of bound. But from a pole zero point of view a differentiator just have zeros ...
Userhanu's user avatar
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Direct and numerically robust conversion from zero-pole to state-space representation

Note: this question was initially asked in a different community. Encouraged by the comments, I decided to cross-post here too. Given (z,p,k) my goal is to convert to a state-space representation (A, ...
DaveC's user avatar
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Finding the region of stability of a system

Suppose we have a closed loop system controlled by some microcontroller $K$ First we take the open loop gain which is $\frac{K}{s(s+6)}$.It has 1 pole at the origin and at $s=6$ and 0 zeros. So we ...
Volpina's user avatar
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2 answers
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Routh's stability condition

Assume we have a LTI system which has poles in the half left plane of the s domain. Before I learnt Routh's stability condition I had imagined that this was enough to decide whether a LTI system was ...
Volpina's user avatar
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How to determine if a system is minimum phase or not?

I'm studying for an exam and this is an old exam question that I don't understand: Is the following system non-minimum phase? $$G(s) = \frac{e^{-2s}}{s+2}$$ I can see that the real part of the pole is ...
student's user avatar
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Can Synchrosqueezing be use to Derive IIR Filter From Impulse Response

I am looking for alternate solutions to determine the IIR filter coefficients from the impulse response, or more specifically determine the closest IIR filter for a given FIR filter. Much of this is ...
Dan Boschen's user avatar
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What is the position of all zeros of a minimum phase, Type 1 Linear Phase FIR Filter?

Let me write down all the facts that I know of. In context of the z plane: Minimum phase system: All zeros and poles of such a system lie inside the unit circle. Linear phase FIR filter: For every ...
McSuperbX1's user avatar
1 vote
2 answers
696 views

How we determine type of filter with pole(s), zero(s)? [duplicate]

Let's say we have this Laplace transform: $$H_{1}(s)=\frac{1}{(s+1)(s+3)}\;, \; \Re{e} (s)>-1 $$ So, we know that there is a poles at $s=-1$ and $s=-3$. With these informations, we found that to be ...
emrexx's user avatar
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1 answer
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Group delay and number of zeros for a symmetric FIR system

I am studying for an exam and need help on a question on the study guide. The question is given below. A symmetric FIR system $h[n]$ extends from $n=7$ to $n=11$. a) What is the group delay? b) How ...
AdamsK's user avatar
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6 votes
1 answer
294 views

Pole Quantization Patterns in 2nd Order IIR Resonators

Background My typical approach to fixed point design for digital filters is to iteratively scale and increase quantization while comparing the fixed point simulation to the floating point design ...
Dan Boschen's user avatar
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2 answers
163 views

How to find zeros of a transfer function

Given the following transfer function, $$H(z) = \frac{6 + 4z^{-1}}{2 + 5z^{-1} - 3z^{-2}}$$ How do we find the zeros of the transfer function? We can write the above expression as $$\frac{3(1+\frac{2}{...
MaxFrost's user avatar
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Significance of poles in a Transfer Function

Sorry for asking this basic question, but I am new to signal processing and have this doubt for a long time. I have been studying signal modelling and have $$H(z) = B_q(z)/A_p(z)$$ where $A_p(z)$ ...
Kuchi Yashwanth's user avatar
1 vote
2 answers
445 views

LPF design with pole/zero placement at rejection at specified freq

I am about to design a low-pass filter with a zero/pole placement method in such a way that rejected frequencies are placed at $500\,\text{Hz}$ and their multiples. Are there any simple instructions ...
user3428154's user avatar
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1 answer
64 views

finding x[0] from the region of convergence

I have the ROC of a signal $x[n]$ with $z$-transform $X(z)$ as below: Now I am wondering how I can find $x[0]$ by not calculating inverse z transform based on the roc, I am looking for a simpler, and ...
Donya's user avatar
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1 vote
1 answer
175 views

Confusions regarding expressions of transfer functions of ideal integrator and ideal differentiator?

The ideal integrator has differentiator has transfer function H(s)= -1/RCs while ideal differentiator has transfer function H(s)= -RCs It is often said regarding above integrator that it has a zero at ...
cvs's user avatar
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2 votes
1 answer
87 views

How does the phase/gain margin method work?

We have the closed loop transfer function: $$T(s)=\frac{L(s)}{1+L(s)}$$ So as far as I understand we check along the $j\omega$-axis on the Bode plot whether $L(s)=-1$, cause that's when $T(s)$ has ...
Kakukk777's user avatar
4 votes
2 answers
1k views

Poles and zeros form of a transfer function

I know that a transfer function for a discrete-time LTI system can be written in the form $$ H(z) = \frac{Y(z)}{X(z)} = \frac { \displaystyle\sum_{m=0}^M {b_m z^{-m}}} {1 + \displaystyle\sum_{n=1}^...
DaBler's user avatar
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2 votes
2 answers
323 views

making a laplace s-domain plot from numerical data to decompose signal into decaying sinusoids

I would like to make a 3D laplace s-domain plot from experimental data I have. The examples I have seen for this are when the function is already known and an analytical solution can be obtained (...
Aaron's user avatar
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5 votes
1 answer
720 views

Why don't unit circle poles lead to infinite amplitude response for Butterworth lowpass?

This is probably a very stupid question. In many places (e.g. here), the Butterworth filters, e.g. lowpass, are described as being "allpole" filters, that have all of these poles on the unit ...
tobalt's user avatar
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3 votes
1 answer
1k views

Specify notch bandwidth by pole placement

I am trying to implement a notch filter by placing zeros and poles. I found in this thread how to specify the frequency to be filtered out (referred to as $\omega_n$ in previous link,) but it is not ...
aheuchamps's user avatar
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1 answer
30 views

Confused with region where root locus lies and sketch

How will be the root locus of $$G(s) = \frac K { (s^2+2s+2)(s^2+2s+5) } $$ look like? The poles will be -1+2i, -1-2i, -1-i, -1+i which lies on the same vertical line and i am confused about the region ...
Nothing's user avatar
1 vote
2 answers
216 views

Scipy tf2zpk doesn't return zeros

I have the following transfer function: $$H(z) =\frac{\alpha z}{(z-(1-\alpha))}$$ I'd like to find zeros and poles of it by scipy.signal.tf2zpk: ...
Curious's user avatar
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0 votes
1 answer
74 views

Find a band-pass filter

The question is: how can I define $h_1[n]$ in such a way that $h [ n ] = \delta [n - 1 ] + 2 \delta [n -2 ] + h_ 1 [n]$ is a band-pass filter. My thought was the following. Firstable, I wrote the $Z$-...
Riesz98's user avatar
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1 vote
1 answer
201 views

Combining multiple bandstop filters works only sometimes

for a school project, we were supposed to filter out 4 rogue cosine waves of a given frequency. I created a filter of my own by choosing zeroes and poles by hand. Here, I made 4 poles and 4 zeroes (...
ampersander's user avatar
0 votes
1 answer
556 views

Find Transfer Function and Appropriate Coefficients of the Transfer Functions from Pole Zero Plot

I got a Transfer function problem and I am confused in finding a solid solution step. Below is the problem description: 1st and 2nd order discrete-time filters with different pole-zero locations shall ...
HaRLoFei's user avatar
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1 answer
156 views

Calculating tranfer function, poles, zeros and impulse response given input and outpul signals in matlab

I have been given an input and output signal. input: x(n)=(0.3^n)*u(n) + (5^n)*u(-n-1) output: y(n)=(3^n)*u(-n-1) - ((2^(n+2))/(3^n))*u(n). or x=(0.3.^n).*(n>=0) + (5.^n). *(n<=-1) --> in ...
Christine's user avatar
1 vote
2 answers
61 views

Filter filters out more than needed

I am currently coding a school assignment. I have a 1.5s recording of someone's speech that has 4 rogue cosines mixed in. With sampling rate 16000Hz, I divided the recording into frames of 1024 ...
ampersander's user avatar
2 votes
2 answers
365 views

Butterworth filter poles

Hi, I'm looking at this textbook question and trying to get a better idea of exactly what its asking. For the processing to be real valued each pole would have to have a complex conjugate right? So ...
Dr. Shakamoto's user avatar
1 vote
3 answers
231 views

How can you see from the transfer function of a system that it has feed forward/feedback elements?

Furthermore, how can you see from the pole/zero plot if the system has feed forward/feedback elements?
BatS00p's user avatar
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2 votes
1 answer
530 views

ROC of $\mathcal{Z}$-Transform and zeros

Theorem: Let $$f(z) = \sum_{n=0}^{+\infty}a_nz^n$$ where $z\in\mathbb{C}$. If $f(z_0)$ exists for some $z_0\in\mathbb{C}$ then it converges for all $z\in\mathbb{C}$ such that $|z|\lt|z_0|$. Proof: It ...
S.H.W's user avatar
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0 votes
1 answer
324 views

Understanding the Chebyshev2 Bandpass Filter Poles-Zeros Plot

EDIT This ended up being a bug with my plotting code :) I'm relatively new to using IIR filters, I wanted a bandpass filter for the 0.5Hz -> 5.0Hz frequency range and was looking at the zero-pole ...
GlitchesEtcEtc's user avatar
0 votes
1 answer
64 views

How to convert passband and stopband frequencies to poles and zeros

I have a NI 9229 digitizer with the following datasheet. The datasheet mentions: a passband frequency of $0.453f_s$ with a flatness of $\le0.1\,\text{dB}$ a stopband frequency of $0.547f_s$ with ...
Badr's user avatar
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0 votes
1 answer
33 views

Zeroes and poles for a system

I have run into some issues on an exercise for the course in signal analysis and systems I am currently studying. We are to create an echo effect and are using the system below: I am to find the ...
Aedrha's user avatar
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0 votes
1 answer
37 views

How to identify from poles and zeros if it is a bandpass

For an example, this is a figure I made from MATLAB, based on the poles and zeros, how can identify if it is a bandpass filter.
jd_01's user avatar
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0 votes
1 answer
256 views

Complex damped exponential signal with repetitive poles and the significance of falling factorial

I was modelling a complex damped exponential signal (discrete) with unique poles as below: \begin{equation} x = \sum_{k=1}^{K} (a_k e^{(j\phi_k)})(e^{\{(j2\pi f_k - \alpha_k)\Delta t\}t}), \quad t ...
Neuling's user avatar
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1 vote
1 answer
71 views

Why RHP zero phase is not 180° to 90°

The asymptotic phase behavior of an RHP zero is from 0 degrees to -90°, the mirror of an LHP zero. Graphically, I'm confused about why this is the case and the phase is not from +180° to +90°. See the ...
Halleff's user avatar
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0 votes
0 answers
111 views

Easiest way to plot phase/amplitude/impulse response for zeros/poles in z-plane

I want to experiment to understand how poles/zeros affect the impulse/amplitude/phase response. So I wonder if there is any software where you can mark poles/zeros and get this? (I have not found any ...
Il De Santa's user avatar
0 votes
1 answer
2k views

Zeros in FIR Filter

I recently had this question in a quiz and was quite confused as I don't think I can assume there are more zeros from just one, so how should I interpret it? Assuming a linear phase FIR filter with ...
HelpMeBro's user avatar
0 votes
1 answer
2k views

Pole Magnitude and Damping Ratio relationship

I know that the damping ratio of a system is defined by the angle of the pole, calculated with respect to the left hand side $x$-axis. Could one infer though, that if the magnitude of the poles is ...
giannis gonidelis's user avatar

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