Questions tagged [poles-zeros]
The poles-zeros tag has no usage guidance.
163
questions
0
votes
1answer
33 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
1answer
27 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 ...
0
votes
1answer
23 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 ...
0
votes
1answer
30 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.
0
votes
1answer
199 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 ...
1
vote
1answer
27 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 ...
0
votes
0answers
26 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
1answer
104 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 ...
0
votes
1answer
78 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
0answers
113 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 ...
4
votes
3answers
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:
$$
\begin{cases}
w[k]+5w[k-1]+6w[k-2]=x[k] \\
y[k]=w[k]+2w[k-1]+3w[k-2]+4w[k-3]
\end{cases}
$$...
0
votes
0answers
48 views
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-...
0
votes
0answers
41 views
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 ...
1
vote
0answers
67 views
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) ...
1
vote
2answers
39 views
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 ...
2
votes
1answer
126 views
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 ...
2
votes
1answer
141 views
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 ...
1
vote
1answer
37 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, $$x(n)= \frac{1}{2\pi j}\oint_c X(z) z^{n-1} \...
1
vote
0answers
64 views
Poles and zeros from step reponse?
Is there a numerically robust method for calculating the poles and zeros of a discrete-time causal LTI SISO system given its response to a unit-step input?
In the specific example I'm working on all ...
1
vote
1answer
67 views
Magnitude response of mirrored (with respect to unit circle) poles and zeros
I just want to check that my understanding about the following paragraph from Optical Filter Design
and Analysis by Christi K. Madsen, Jian H. Zhao is correct:
A filter’s magnitude response is equal ...
5
votes
2answers
156 views
Uncountable Set of Poles?
It is easy to define an (ideal) LTI system that would have an infinite number of poles - for instance, if the transfer function is
$$
H(z)=\frac{1}{\cos(z)-1}
$$
However, this would only define a ...
2
votes
2answers
102 views
Laplace Transform: zeros and corresponding impulse response $h(t)$
Poles and the impulse response
If our impulse response is in the form :
$$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)...
3
votes
2answers
90 views
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 :
$$h(t) = Ae^{-\sigma_0t}\cos(\omega_0t+\...
0
votes
0answers
68 views
Transfer function model to frequency response
I have a problem, I wanted to filter the signal with a Butterworth filter built on the basis of a prototype. I have zeros and poles and an $H (s)$ answer, and I do not have the frequency response. How ...
0
votes
1answer
42 views
What does poles in unit circles center mean?
Suppose i have all my poles in unit circle center. What kind of information this gives me?
Can i determine if this filter is IIR or FIR?
0
votes
0answers
19 views
Stability of $x(n) = A x(n-1)+b$
I am looking at the following system:
$x(n) = A x(n-1) + b$
where x and b are vectors and A is a matrix. How can I derive the stability and causality conditions for such a system using Z transform?
If ...
0
votes
1answer
47 views
ROC of Z transform Doesnt include a pole on the boundary?
I cannot figure out what is going on here. I have an example problem in my book that says the ROC of a certain function is $$ 0.5 < |z| < \infty$$
The function's denominator is $$ 1 - z^{-1} + 0....
0
votes
2answers
49 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 ...
0
votes
1answer
69 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
679 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
votes
1answer
100 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 ...
0
votes
0answers
37 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
0
votes
0answers
133 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
votes
1answer
86 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
votes
2answers
43 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 ...
3
votes
4answers
675 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
votes
2answers
352 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
vote
1answer
282 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
vote
3answers
303 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 ...
1
vote
3answers
606 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
votes
1answer
48 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
votes
1answer
108 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
votes
1answer
91 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 ...
3
votes
1answer
101 views
What does it mean that a zero is slow?
I am studying control systems, and have encountered the definition of a slow zero. I am searching on internet and in books, but I don't understand the meaning this. I know that if a zero is too slow, ...
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
votes
1answer
106 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
vote
1answer
217 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
684 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
540 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 ...
3
votes
1answer
1k 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 ...
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