Skip to main content
Share Your Experience: Take the 2024 Developer Survey

Questions tagged [poles-zeros]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0 votes
1 answer
60 views

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 ...
0 votes
0 answers
29 views

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 ...
2 votes
3 answers
309 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 transform which maps the $s$-...
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 ...
0 votes
1 answer
251 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 ...
2 votes
0 answers
46 views

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 ...
0 votes
1 answer
135 views

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 ...
3 votes
6 answers
3k 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 ?...
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 $$...
1 vote
1 answer
90 views

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 ...
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 ...
1 vote
1 answer
150 views

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 ...
1 vote
0 answers
58 views

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
0 votes
0 answers
49 views

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 ...
1 vote
3 answers
115 views

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 ...
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 ...
2 votes
0 answers
49 views

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, ...
0 votes
2 answers
40 views

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 ...
0 votes
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 ...
1 vote
1 answer
191 views

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 ...
0 votes
1 answer
279 views

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 ...
2 votes
0 answers
65 views

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 ...
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 (...
1 vote
2 answers
695 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 ...
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 ...
3 votes
1 answer
276 views

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 ...
0 votes
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}{...
2 votes
2 answers
2k views

Minimum number of Poles and zero of transfer function H(z)?

Suppose $G(z)=H(z)(1-\frac{1}{2}z^{-1})$ now in question its saying ROC of G(Z) is entire Z plane except Z=0,so here we need not to add anything because G(Z) already a right sided signal with ROC ...
1 vote
2 answers
442 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 ...
2 votes
2 answers
261 views

How to determine number of poles or zeros in prony's method?

I would like to use Prony's method for signal modelling. I want to design a filter such that its impulse response is equal to the message signal. I use the function ...
0 votes
1 answer
48 views

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 $A_p(z)$ ...
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 ...
-1 votes
2 answers
92 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 ...
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 ...
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}^...
0 votes
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 ...
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 ...
10 votes
4 answers
14k views

What is the difference between natural response and zero input response?

I am new to DSP and was going through different responses of a system subjected to an input. My understanding of zero input response is: it is the response/output of the system when the input signal ...
0 votes
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 ...
-1 votes
1 answer
1k views

How do I find the ROC of a system if it has no poles

The output of a system of discrete time $y[n]$ is corellated with the input $x[n]$ through the equation $y[n]$. $$y[n] = \frac 13\big(x[n-1]+x[n]+x[n+1]\big)$$ It then asks me to find the system ...
-1 votes
2 answers
1k 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 ...
-1 votes
1 answer
487 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 ...
-1 votes
1 answer
684 views

Pole zero plot, normalizing frequency response plot?

I'm asked to plot the frequency response (amplitude) given a specific pole-zero diagram. $$ H(z) = H_0 \frac{\prod\limits_{m=1}^{M} (z - q_m)}{\prod\limits_{m=1}^{M} (z - p_m)}$$ $$ H(e^{i\omega}) =...
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: ...
-1 votes
1 answer
667 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
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 $Z$-...
0 votes
1 answer
555 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 ...
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 (...
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 ...
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 ...

1
2 3 4 5