Questions tagged [poles-zeros]

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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 ...
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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 ...
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43 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 ...
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1answer
44 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 ...
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1answer
46 views

Difference between repeated poles and non repeated 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 ...
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1answer
87 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 ...
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1answer
63 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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1answer
151 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/...
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1answer
74 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, ...
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1answer
36 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 -...
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1answer
371 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 ...
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1answer
393 views

Effect of origin poles on stability?

What will be stability if we have only one single pole at origin in s domain?? and what will be the case for multiple poles at origin in s domain?
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19 views

Factoring digital IIR filter as a causal and anticausal pass?

Background: I'm new to signal processing and I'm reading some papers on B-spline interpolation of digital signals and trying to understand how a computation is derived. If I'm given samples from some ...
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1answer
61 views

How can the Poles of the Root Locus be negative?

My understanding of drawing a root locus diagram is that stability requires all roots of the characteristic polynomial of the open loop transfer function to lie in the negative real part of the plane. ...
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1answer
199 views

Poles and zeros map, High pass filter

Given the following poles and zeros map I have to identify qualitatively, which filter type is represented (Low-Pass, High-Pass, ...). In the solution it says, that this is a high pass filter. ...
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33 views

Powers of $z$ in a discrete transfer function

I have been working with discrete-time systems and I am not yet able to understand the reason behind using powers of $z^{-1}$ in transfer functions. I get that $z^{-1}$ means a delay, but when we ...
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1answer
210 views

pole/zero plot & impulse response

in a mock exam of dsp was asked this question, and even in knowing how to compute DFT's of the plot, I wondered if there was a fast way of pairing these plots to their respective impulse response? ...
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1answer
52 views

How to design a a filter and how to determine the poles and zeros on the basis of following informations?

A sinusoidal signal of 300Hz frequency,3V amplitude is contaminated with line frequency (50Hz,1V). Design a digital filter including poles and zeros to remove the interference component. Consider the ...
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70 views

Where to start in the design of my filter to remove 50 Hz

pick any 3 random files from this database, : https://physionet.org/pn3/ecgiddb/ They are subject to 50 Hz powerline interference. We wish to convert from time domain to frequency domain and remove ...
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2answers
298 views

Z transform - Inverse System function - Why number of poles and zeros myst be equal?

I know that if a system is causal then the system function H(z) must have : a) a ROC that spans from the exterior of the most distant pole and b) the number of zeros must not be greater than the ...
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33 views

The range of r can be r<1 and r>1

I have to find the range of r which makes H(z) stable. There is no restriction of left sided or right sided. Then, both r<1 (z>r) and r > 1 can be the answer?
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1answer
23 views

Plane Settings of the Matched $z$-transform Method

I've come across that the matched $z$-transform maps poles of the $s$-plane design to locations in the $z$-plane. My question is, what is the $s$-plane and what does this mean? I'm aware that the ...
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1answer
535 views

Nyquist Plot for transfer functions with poles at the origin

I'm learning Nyquist plots and something has been seriously bugging me when treating poles or zeros in the origin. Nyquist plots obtains information based on the argument principle which states "If f(...
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36 views

Determining type of analog filter given its pole zero plot

How can i classify an analog filter given its pole zero map. For example: I've got my zero's located at $±2j$ and my poles located at $-1$ & $-2$ , then what is the nature of the filter? $ i.e, ...
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2answers
476 views

Pole-zeros of a real-valued causal FIR system

Could someone please help me with the following question? Below is the magnitude response of a real-valued causal linear phase FIR system of order N = 6. Determine the location of poles and zeros. I ...
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2answers
400 views

How to determine if a filter is bandpass/stopband from its pole-zero diagram in z-domain

How can we determine if a filter is bandpass or stopband, just by looking at its pole-zero diagram in z-domain? For exmaple, if we have a system with third-order pole at the origin and a zero on the ...
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0answers
18 views

Pole location in linear prediction of sinusoidal signal

As mentioned in texts [Ref: Vaidyanathan P.P, The Theory of Linear Prediction], that a process which is perfectly an AR(p) process, or a sinusoidal process, can be perfectly reconstructed through ...
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1answer
238 views

Phase contribution of complex poles

I am struggling with understanding the phase contribution of each individual pole. Let's say we have a system (minimum-phase system if it makes a difference) and it has poles located at: and What is ...
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122 views

Determine phase response from pole-zero plot

I know how to determine the frequency response from the pole-zero diagram given the following formula: $\left | H(f) \right | = \frac{\prod \left | (e^{j2\pi f} - a_{i})\right |}{\prod \left | (e^{...
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101 views

Poles and zeros representation in s-plane

We have a filter (or a system) that has two poles at $f_{p1} = f_{p2} = 20$ GHz and one zero at $f_{z1} = 15$ GHz. Let's assume the gain is $K = 1$. Then how do you mark these poles and zero in the ...
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1answer
118 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 ...
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1answer
64 views

Hidden zero in system equation $H(z)$

An FIR linear phase filter has unit sample response $h[n]$ that is real with $h[n]=0$ for $n < 0$ and $n > 7$. If $h[0]=1$ and the system function has a zero at $z=0.4e^{j\pi/3}$ and a zero at $...
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1answer
43 views

Does the system function H(z) for a filter always have symmetry above and below the real x-axis?

When I look at the Pole/Zero diagrams in the DSP books it appears that whatever pole or zero is above the real x-axis from: $$\omega=0 \rightarrow \pi$$ is always reflected as a mirror image ...
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1answer
400 views

Is the inverse of a causal system also causal?

If I have a causal system H(z) and I find the inverse of this system: $$ G(z) = \frac{1}{H(z)} $$ Is G(z) also causal?
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336 views

Get the discrete-time poles and zeros from continuous-time poles and zeros

How do you implement the following function: $$[Z^d, P^d, K^d] = \text{fcn} \,(Z^c, P^c, K^c),$$ where $Z^c = [z^c_m, ..., z^c_1]$, $P^c = [p^c_m, ..., p^c_1]$, and $K^c$ are zeros, poles, and gain ...
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1answer
198 views

Determine poles and zeros of a specific filter design

I have a design question and need to determine poles-zeros of a IIR bandpass filter. Requirements are: 1-order should be 3 2-causal 3-real valued impulse response 4-stable 5-cutoff freq: pi/3-pi/...
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1answer
162 views

Octave - freqz strange results

I wrote octave code to find transmittance based on zeros and poles: ...
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1answer
279 views

Determining asymptotic stability using transfer function?

In an exam task, I am asked to determine the transfer function of the following direct-time system and decide whether it's stable. I think this system is canonical and the amplifiers 'on top' ...
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1answer
337 views

Trivial and non-trivial zeros

I am new to DSP, and I'm self studying. Could someone please explain to me what do we mean by trivial and non-trivial zeros?
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2answers
764 views

Stability of system with poles inside unit circle - conflict with differential equation

I am trying to understand why a system with a single pole inside the unit circle is stable. For example, take a system with one pole at $z=\frac{1}{2}$. The literature says the system is stable. As a ...
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1answer
985 views

How to determine poles and zeros of the z-transform?

This is a simple question, but I just don't understand how we determine the poles and zeros of a rational system function. For example, for the LTI system described by this constant coefficient ...
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1answer
561 views

How can I determine the order of filter?

This is my first study about signal analysing. I'm very confused about filter order. My problem is how can I know whether its 12-th order, or 2nd order like the book says so? I already knew that slope ...
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1answer
396 views

IIR filter design fitting step response

I have access to the step response of a system and I want to find its poles and zeros without knowing the order of the system. Consider an example of a step response of the system shown in the ...
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1answer
679 views

Poles and zeros map

Given the following map of poles and zeros for some $H^L(s)$: How can I understand from the map that the given Transfer function is LPF? Hence the poles are located at the hight frequencies it should ...
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1answer
107 views

Poles of the transfer function in Z Transform

Given that: $H(z)$ has 4 poles maximum. $H(z)$ has a pole at $z_1=a+bi$ Given that the impulse response $h[n]$ is: Symmetric: $h[n] = h[-n]$ Real: $\forall$$n$ , $h[n]$$\in$$\mathbb{R}$ How we can ...
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1answer
597 views

BIBO Stability for system with no poles

I have two questions regarding systems with no poles: Why does a system with no poles have a finite support? Why if the system has a finite support it means that it is BIBO stable?
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1answer
107 views

What happens when the poles of this z-transform function are outside the ROC for a signal?

I am given a z-transform function for a signal $h[n]$. It's $H(z)=\frac{2z^2-0.75z}{(z-0.25)(z-0.5)}$. I am supposed to find $h[n]$ and check the stability of the system for these cases: a)ROC: $|...
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3answers
654 views

How to find difference equation, given poles and zeros?

I'm given poles at ${1+i}$ and ${1-i}$, and zero at $0$. I have to find the difference equation and find out whether the system is stable. Now I found in a similar question, which structure I tried ...
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1answer
711 views

How to plot the poles and zeros of this Bandpass Filter in MATLAB?

So I'm trying to design a band pass filter in MATLAB (with a center frequency of 10kHz and a sampling frequency of 44kHz). I have calculated the transfer function but I'm not sure how to enter this ...
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1answer
72 views

Find a stable transfer function $G(z)$ such that $|G(z)| = |H(z)|$

Consider the following causal IIR transfer function: $$ H(z) = \frac{2z^3 - 4z^2 + 9}{(z-3)(z^2+z+0.5)} $$ Is $H(z)$ a stable function? If it is not stable, find a stable transfer function $G(z)...