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Questions tagged [poles-zeros]

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1answer
25 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 ...
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0answers
25 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 ...
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1answer
65 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
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1answer
67 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 ...
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0answers
71 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 ...
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3answers
963 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: $$ \begin{cases} w[k]+5w[k-1]+6w[k-2]=x[k] \\ y[k]=w[k]+2w[k-1]+3w[k-2]+4w[k-3] \end{cases} $$...
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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-...
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0answers
40 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
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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) ...
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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
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1answer
87 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
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1answer
133 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
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1answer
32 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} \...
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0answers
59 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
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1answer
56 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
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2answers
153 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
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2answers
93 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)...
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2answers
73 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+\...
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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
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1answer
41 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?
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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
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1answer
40 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....
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2answers
46 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 ...
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1answer
63 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
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2answers
458 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 ...
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1answer
96 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
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0answers
36 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
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0answers
40 views

Why does the filtered signal amplitude increase exponentially?

I am new to signal processing. I am having a problem applying a filter to a test signal. I am working with MatLab. My test signal is a chirp up to Nyquist frequency and my filter is in zeros and poles ...
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0answers
104 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
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1answer
63 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 (...
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2answers
38 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
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4answers
535 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
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2answers
269 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
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1answer
245 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
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3answers
241 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 ...
0
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3answers
488 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
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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
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1answer
93 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
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1answer
74 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
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1answer
91 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
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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
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1answer
94 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
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1answer
178 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
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1answer
585 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
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1answer
467 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
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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 ...
1
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1answer
1k views

Pole Zero plot given a Transfer function

I've been looking at how to plot zeros/poles based on a transfer function. I found a couple of Tutorials online. In the first youtube tutorial, the author brilliantly explains how to plot the zeros/...
0
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1answer
254 views

Are MATLAB function zp2tf() and tf2zp() are complementary or not?

I was under impression that given, pole, zero and gain the transfer function (filter coefficients b and a) is fixed. Therefore, ...
0
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1answer
96 views

Find the length of the impulse response of a Linear Phase Type 4 FIR filter

The length should be found such that the group delay is minimum It is given that the impulse response is real. One zero of the Transfer function is at $0.6e^{j\frac{\pi}{4}}$, and another one is at -...
1
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1answer
1k views

How to realize Poles and zeros at infinity??especially through transfer function?

I have a question regarding the poles and zeros at infinity I often read here in DSP SE and also in some textbooks about poles and zeros at infinity This question also answers somehow (but not in ...