Questions tagged [poles-zeros]
The poles-zeros tag has no usage guidance.
178
questions
2
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1
answer
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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 ...
- 21
4
votes
2
answers
693
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
$$
H(z) = \frac{Y(z)}{X(z)} = \frac
{ \displaystyle\sum_{m=0}^M {b_m z^{-m}}}
{1 + \displaystyle\sum_{n=1}^...
- 206
2
votes
1
answer
45
views
making a laplace s-domain plot from numerical data to decompose signal into decaying sinusoids
I would like to make a 3D laplace s-domain plot from experimental data I have. The examples I have seen for this are when the function is already known and an analytical solution can be obtained (...
- 21
5
votes
1
answer
628
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Why don't unit circle poles lead to infinite amplitude response for Butterworth lowpass?
This is probably a very stupid question. In many places (e.g. here), the Butterworth filters, e.g. lowpass, are described as being "allpole" filters, that have all of these poles on the unit ...
- 312
2
votes
1
answer
116
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Specify notch bandwidth by pole placement
I am trying to implement a notch filter by placing zeros and poles. I found in this thread how to specify the frequency to be filtered out (referred to as $\omega_n$ in previous link,) but it is not ...
- 23
0
votes
1
answer
25
views
Confused with region where root locus lies and sketch
How will be the root locus of
$$G(s) = \frac K {
(s^2+2s+2)(s^2+2s+5)
}
$$
look like?
The poles will be -1+2i, -1-2i, -1-i, -1+i which lies on the same vertical line and i am confused about the region ...
- 1
1
vote
2
answers
46
views
Scipy tf2zpk doesn't return zeros
I have the following transfer function:
$$H(z) =\frac{\alpha z}{(z-(1-\alpha))}$$
I'd like to find zeros and poles of it by scipy.signal.tf2zpk:
...
- 63
0
votes
1
answer
57
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$-...
- 57
1
vote
1
answer
32
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 (...
- 133
0
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1
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79
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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 ...
- 101
0
votes
1
answer
83
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 ...
1
vote
2
answers
51
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 ...
- 133
2
votes
2
answers
120
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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 ...
1
vote
3
answers
39
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?
- 11
2
votes
1
answer
106
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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 ...
- 701
0
votes
1
answer
89
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 ...
0
votes
1
answer
39
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 ...
- 3
0
votes
1
answer
29
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 ...
- 53
0
votes
1
answer
32
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.
- 3
0
votes
1
answer
231
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 ...
- 69
1
vote
1
answer
36
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 ...
- 261
0
votes
0
answers
55
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 ...
0
votes
1
answer
452
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 ...
- 37
0
votes
1
answer
181
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 ...
0
votes
0
answers
258
views
How to calculate the magnitude of frequency response from Pole zero plot
I have checked the theory to calculate the magnitude of frequency response from the pole-zero plot from the previous posts. As far as I understand(and I hope I am correct), the magnitude can be ...
- 115
4
votes
3
answers
1k
views
Is this system causal or not?
My efforts of solving this question are below.
I came to a conclusion that this system is causal, since:
$$
\begin{cases}
w[k]+5w[k-1]+6w[k-2]=x[k] \\
y[k]=w[k]+2w[k-1]+3w[k-2]+4w[k-3]
\end{cases}
$$...
- 145
0
votes
0
answers
60
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How to break a second-order filter into two first-order filter
Let's assume the transfer function of a continuous-domain filter consists of two poles and one zero:
$H(s) = \frac{k_c (s-\omega_{z_1})}{(s-\omega_{p_1})(s-\omega_{p_2})}$.
Let's consider we do the bi-...
- 188
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0
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56
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How to design IIR digital filters
Practical Infinite-Impulse-Response (IIR) filters are usually based upon analogue equivalents (Butterworth, Chebyshev, etc.), using a transformation known as the bilinear transformation which maps the ...
- 188
1
vote
0
answers
70
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Implementation of IIR filter
Suppose we have a discrete input waveform (with sampling frequency Fs = 32*56e9). We want to filter this waveform with a filter that has two complex conjugate poles (at 22 GHz) and one zero (at 17GHz) ...
- 188
1
vote
2
answers
45
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Why can the number of zeros be no more than the number of delay elements in a signal flow network?
Let $N$ be the signal graph representation network of the system function (in rationale form) of a discrete-time LTI system. For a network $N$ with
no loops, the impulse response is no longer than ...
- 325
2
votes
1
answer
365
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What is the reason behind complex conjugate pairs in Linear Phase FIR filter analysis from the Pole Zero plot
When we say that a Generalized Linear Phase System must satisfy the pole zero plot with the condition that a complex zero not on the unit circle exist's in a pair of 4. Then I understand that I need ...
- 33
2
votes
1
answer
180
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Ending points of the root locus
Let $$D(s) + KN(s) = 0 \tag{1}$$where $D(s)$ and $N(s)$ are polynomials of $s \in \mathbb{C}$ such that $\text{Deg}(D) = n, \ \text{Deg}(N) = m$ and $n\ge m$. The root locus method tells us how the ...
- 701
1
vote
1
answer
50
views
confusion related to finding inverse Z-Transform using Complex Integral Method
I am facing problems related to evaluation of inverse Z-Transform using Complex Integral Method;
Consider $X(z)=\frac{z}{z-2} $ and $ROC: |z|>2$
then, $$x(n)= \frac{1}{2\pi j}\oint_c X(z) z^{n-1} \...
- 275
1
vote
0
answers
120
views
Poles and zeros from step reponse?
Is there a numerically robust method for calculating the poles and zeros of a discrete-time causal LTI SISO system given its response to a unit-step input?
In the specific example I'm working on all ...
- 111
1
vote
1
answer
102
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Magnitude response of mirrored (with respect to unit circle) poles and zeros
I just want to check that my understanding about the following paragraph from Optical Filter Design
and Analysis by Christi K. Madsen, Jian H. Zhao is correct:
A filter’s magnitude response is equal ...
5
votes
2
answers
171
views
Uncountable Set of Poles?
It is easy to define an (ideal) LTI system that would have an infinite number of poles - for instance, if the transfer function is
$$
H(z)=\frac{1}{\cos(z)-1}
$$
However, this would only define a ...
- 51
2
votes
2
answers
182
views
Laplace Transform: zeros and corresponding impulse response $h(t)$
Poles and the impulse response
If our impulse response is in the form :
$$h(t) = e^{-\sigma_0 t}\cos(\omega_0 t) \, u(t)$$
(where $u(t)$ is the unit step function)
And its Laplace transform is :
$$H(s)...
- 73
3
votes
2
answers
151
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Laplace transform : integral vs poles & zeros
If Laplace transform is expressed as :
$$\int_{-\infty}^{+\infty} h(t)e^{-st}dt $$
with :
$$s = \sigma + j\omega$$
and $h(t)$ an impulse response expressed as :
$$h(t) = Ae^{-\sigma_0t}\cos(\omega_0t+\...
- 73
0
votes
0
answers
74
views
Transfer function model to frequency response
I have a problem, I wanted to filter the signal with a Butterworth filter built on the basis of a prototype. I have zeros and poles and an $H (s)$ answer, and I do not have the frequency response. How ...
0
votes
1
answer
59
views
What does poles in unit circles center mean?
Suppose i have all my poles in unit circle center. What kind of information this gives me?
Can i determine if this filter is IIR or FIR?
- 3
0
votes
0
answers
21
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
votes
1
answer
65
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....
- 61
0
votes
2
answers
62
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 $1+𝑎_1𝑧^{−1}+𝑎_2𝑧^{−2}=0$, then for the roots to be inside the unit circle (i.e. in the unit disk), the ...
- 3
0
votes
1
answer
95
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
3
votes
2
answers
1k
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 ...
- 701
0
votes
1
answer
144
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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 ...
- 861
0
votes
1
answer
115
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Is it a mandatory condition that complex poles and zeros should always exist as conjugate pairs?
Complex poles and zeros always exist in conjugate pairs?If not always, in which context applicable?
https://www.informit.com/articles/article.aspx?p=32090&seqNum=9
The above link mentions related ...
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0
votes
0
answers
210
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 ...
- 13
-1
votes
1
answer
222
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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 (...
- 3
-1
votes
2
answers
82
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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