Questions tagged [poles-zeros]
The poles-zeros tag has no usage guidance.
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1answer
42 views
Octave - freqz strange results
I wrote octave code to find transmittance based on zeros and poles:
...
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0answers
29 views
How to filter a discrete waveform by having continuous domain poles and zeros
Let's consider we want to model a continuous time filter that has one zero at 30GH and two poles at 35GHz.
I also have a sampled waveform with sampling frequency of $f_s$, so the time interval ...
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1answer
30 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
26 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
69 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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0answers
43 views
Depending on how a system function is written, will it always have the same zeros and poles?
There are many ways to write a system function. In terms of direct forms, cascade, parallel, transposed. Also the system function depends on if you write the poles and zeros in terms of $1+az^{-1}$ or ...
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1answer
37 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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0answers
17 views
Equality of the Number of Poles and Zeros [duplicate]
In which case number of poles and zeros on the z-plane are equal? Some say it is because of causality but for the causal case, it is stated that the number of zeros cannot be greater than the number ...
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1answer
67 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
151 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
48 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 ...
1
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1answer
38 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$$\mathbb{R}$
How we can ...
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1answer
86 views
BIBO Stability for system with no poles
I have two questions regarding systems with no poles:
Why does a system with no poles have a finite support?
Why if the system has a finite support it means that it is BIBO
stable?
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1answer
46 views
What happens when the poles of this z-transform function are outside the ROC for a signal?
I am given a z-transform function for a signal $h[n]$. It's $H(z)=\frac{2z^2-0.75z}{(z-0.25)(z-0.5)}$. I am supposed to find $h[n]$ and check the stability of the system for these cases:
a)ROC: $|...
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2answers
93 views
How to find difference equation, given poles and zeros?
I'm given poles at ${1+i}$ and ${1-i}$, and zero at $0$.
I have to find the difference equation and find out whether the system is stable.
Now I found in a similar question, which structure I tried ...
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1answer
257 views
How to plot the poles and zeros of this Bandpass Filter in MATLAB?
So I'm trying to design a band pass filter in MATLAB (with a center frequency of 10kHz and a sampling frequency of 44kHz).
I have calculated the transfer function but I'm not sure how to enter this ...
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1answer
54 views
Find a stable transfer function $G(z)$ such that $|G(z)| = |H(z)|$
Consider the following causal IIR transfer function:
$$ H(z) = \frac{2z^3 - 4z^2 + 9}{(z-3)(z^2+z+0.5)} $$
Is $H(z)$ a stable function? If it is not stable, find a stable transfer function $G(z)...
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1answer
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1answer
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Poles and zeros in time domain of analogs filters
I am currently studying two Butterworth and Chebyshev low-pass filters of order $n =3$ and $n=2$ respectively, whcih are in fact two prototypes to make a bandpass filter. The transfer function that I ...
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83 views
Simple Pole-Zero placement bandpass filter doesn't work in MATLAB
I'm trying to make a simple bandpass filter using Pole-Zero Placement method, which has unity gain at frequency w=0.37pi and 3 dB cutoff frequency wc=0.42pi (has a gain of 1/sqrt(2) at that frequency)....
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1answer
137 views
Pole zero plot, normalizing frequency response plot?
I'm asked to plot the frequency response (amplitude) given a specific pole-zero diagram.
$$ 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}) =...
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1answer
107 views
Design a filter which passes all frequencies except $\omega=\pm\frac{\pi}{2}$ and plot its pole-zero diagram
Also draw its normalized frequency response.
What is the ROC?
This has to be done in z-plane so there must be two poles at $+i$ and $-i$ since they cannot be included in region of convergence. Is my ...
1
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1answer
46 views
Question about poles and zeros in AR filter
For AR HP filter
zeros, to the right of the imaginary axis
poles outside the unit-circle
zeros on the real axis
poles, to the left of the imaginary axis
Apparently, the right answer ...
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1answer
109 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 ...
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1answer
159 views
Butterworth low pass filter zeros location after bilinear transformation explanation
I am studying in a text book the transformation of a continuous time Butterworth low pass filter into a discrete time filter by means of bilinear transformation:
$$
s = \frac{2}{T_d}*\frac{1-z^{-1}...
1
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1answer
63 views
Drawing the modulus from a Transfer function
As you may guess from my other questions i am a student so pardon me any ignorance and guide me to the truth. Thanks
In this exercise from an exam i was given that transfer function with poles and ...
0
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1answer
50 views
How to determine the poles from a graph
From my knowledge of stability, I understand that if the function approaches a finite number then the system will be stable. Thus if a system is stable its poles will be on the left of the $j\omega$-...
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1answer
334 views
Impulse response function from pole-zero graph
I know that that the poles of this system are: $s_1 = -1 + 2j$ and $s_2 = -1 - 2j$. I think to solve this problem I would need to find the laplace of this plot, with the formula:
$$
W(s) = \frac{\rm ...
3
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1answer
271 views
For a system to be causal, number of finite zeros <= number of finite poles. Why?
I read in this pdf that for a system to be causal, the number of finite zeros must be no greater than number of finite poles. Why?
I know that for a system to be causal, $h[n]=0$ for all $n<0$. ...
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2answers
163 views
What are poles and zeroes (with respect to the inputs and outputs of a system)?
I get it, about poles and zeroes, when we talk in terms of the transfer function.
But, if the transfer function is the ratio of the output to the input, then if the input signal is zero, then the ...
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1answer
58 views
Create an input so that poles show up as outputs?
Let's say we have a rational, causal, stable LTI system with transfer function
$$H(z) = \frac{A(z)}{B(z)}$$
If $H(z)$ has $N$ poles, we can in theory have only 1 of those poles, $p_i$, show up at the ...
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2answers
159 views
Invertibility of Room Impulse Response: Reproducing Research Paper
I have been trying to reproduce this paper¹. Few things which are unclear to me. The paper talks about finding whether a given Room Impulse Response(RIR) is invertible or not based on Nyquist plot.
...
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1answer
5k views
Position of poles and Stability in $z$ domain
We know in Laplace Transform, if the poles lie on the left of $j\omega$ axis, we can say the system is stable. Similarly can we comment on the stability based on poles position in $\mathcal Z$-...
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2answers
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which filters are these?
Location of poles are given in unity circle and 4 zeros are given at origin for every plot,How to check which plot shows which filters?
For the Option (C) i am doing like this
I can write the ...
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1answer
589 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 ...
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1answer
247 views
Why zeroes near the unit circle cause a dip in frequency response, while poles cause a peak?
I have an exam tomorrow and I really can't figure out the question in the title.
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0answers
37 views
Solve for transfer function coefficients embedded in a non-linear system
Given a complex input signal $x$ and real input signal $v$, a 4th order (for simplicity) transfer function $H(z)$ is first applied to $v$ to obtain $w$, which in the time domain is represented by the ...
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1answer
299 views
Calculating poles with complex numbers and quadratic equation
given: $z^2 + 0.8 \sqrt2 z + 0.64 = 0 $
Then, I am using the quadratic equation:
$ z_{1,2} = \frac{-0.8 \sqrt2 \pm \sqrt{(0.8\sqrt2)^2-4 \cdot 0.64}}{2} $
Wolfram Alpha says it the end there should ...
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1answer
463 views
How to check if the poles of transfer function are stable?
$$H(z)=\frac{az}{[z-(b+ja)][z-(b-ja)]}$$
The two poles are looking like this:
$z_{\inf, 1}=b+ja, z_{\inf, 2}=b-ja$
I know they must be inside the unit circle: $|z_{\inf,i}|<1$
So I replace the ...
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2answers
1k views
Transposed Direct Form II VS Direct Form II IIR filters?
I read in "Discrete-Time Signal Processing" Reference, in transposed Direct Form II filters section, that it implements zeros first then poles(unlike Direct form II which implements poles first), ...
3
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2answers
94 views
Finite length truncated exponential sequence $\mathcal Z$-transform, zeros over circle explanation
I'm looking at an example on how to obtain the $\mathcal Z$-transform from a finite length truncated exponential sequence, namely:
$$x[n] =
\begin{cases}
a^N &\text{for} & 0 \leq n \leq N-1\\...
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2answers
997 views
Conjugate reciprocal pairs of zeros and poles in FIR design
Assuming the impulse response $h[n]$ of an FIR filter is real for all $n$,
Why are zeros and poles in FIR design found in reciprocal and conjugate pairs?
Is the assumption necessary for this ...
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1answer
4k views
Filter design with zero - pole placement method
I have some question for you about Filter design.
Α. Calculate the transfer function in order to stop the frequency of $300\textrm{ Hz}$ for sampling frequency at $12\textrm{ kHz}$. Use the
zero – ...
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1answer
1k views
Poles and zeros of a transfer function
What are the poles and zeros of this transfer function (in $z$):
$$H(z)=z+2+z^{-1}$$
and how would you approach the resolution of such problem?
Personally, I would write
$$H(z)=\displaystyle\frac{...
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2answers
691 views
A question about the meaning of pole in time domain
Lets say I have a transfer function $H(s)$ of a system defined in $s$-domain as:
$$H(s) = \frac{1}{s - (-1-j)}$$
So I conclude that the pole on the $s$-plane is where $s = 1+j$. So far so good.
Now ...
1
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1answer
326 views
How do I go from LPC coefficients to a filter polynomial?
I've recently begun experimenting with LPC, and while I understand that it works, I'm still slightly lost on why it works.
Specifically, I understand that LPC involves finding coefficients $a_1, a_2, ...
0
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1answer
124 views
Conjugate Pole Pairs
I am currently studying for an exam for a Speech Processing course I am taking and stumbled across this question in one of the sample exams:
I began to plot the pole-zero configuration placing my ...
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1answer
33 views
Pole-Zero Configuration of Glottal Signal
I am currently studying for an exam in my Speech Processing course this Friday and I stumbled upon this question in one of the sample exams:
The answer to this question was given as:
Can someone ...
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2answers
6k views
determining type of filter given its pole zero plot
How can I classify a filter given its pole-zero map. For example I've got my zero's located at $\pm j$ and my poles located at $\pm\frac{1}{2}j$.
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1answer
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Poles and zeroes - $\mathcal Z$-transform
I just have a small question, something that I am unsure about. I have a difference equation for a filter:
$$y[n] = x[n] - x[n-1]$$
I have worked out the $\mathcal Z$-transform:
$$\mathcal Z\left\...
