Questions tagged [poles-zeros]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
2 votes
1 answer
39 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 ...
user avatar
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}^...
user avatar
  • 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 (...
user avatar
  • 21
5 votes
1 answer
628 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 ...
user avatar
  • 312
2 votes
1 answer
116 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 ...
user avatar
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 ...
user avatar
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: ...
user avatar
  • 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 $Z$-...
user avatar
  • 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 (...
user avatar
0 votes
1 answer
79 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 ...
user avatar
  • 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 ...
user avatar
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 ...
user avatar
2 votes
2 answers
120 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 ...
user avatar
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?
user avatar
  • 11
2 votes
1 answer
106 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 ...
user avatar
  • 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 ...
user avatar
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 ...
user avatar
  • 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 ...
user avatar
  • 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.
user avatar
  • 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 ...
user avatar
  • 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 ...
user avatar
  • 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 ...
user avatar
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 ...
user avatar
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 ...
user avatar
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 ...
user avatar
  • 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: $$ \begin{cases} w[k]+5w[k-1]+6w[k-2]=x[k] \\ y[k]=w[k]+2w[k-1]+3w[k-2]+4w[k-3] \end{cases} $$...
user avatar
  • 145
0 votes
0 answers
60 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-...
user avatar
  • 188
0 votes
0 answers
56 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 ...
user avatar
  • 188
1 vote
0 answers
70 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) ...
user avatar
  • 188
1 vote
2 answers
45 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 ...
user avatar
2 votes
1 answer
365 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 ...
user avatar
2 votes
1 answer
180 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 ...
user avatar
  • 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} \...
user avatar
  • 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 ...
user avatar
1 vote
1 answer
102 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 ...
user avatar
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 ...
user avatar
  • 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)...
user avatar
  • 73
3 votes
2 answers
151 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+\...
user avatar
  • 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 ...
user avatar
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?
user avatar
  • 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 ...
user avatar
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....
user avatar
  • 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 ...
user avatar
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 ...
user avatar
  • 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 ...
user avatar
  • 701
0 votes
1 answer
144 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 ...
user avatar
  • 861
0 votes
1 answer
115 views

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 ...
user avatar
  • 861
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 ...
user avatar
-1 votes
1 answer
222 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 (...
user avatar
  • 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 ...
user avatar
  • 188