Questions tagged [poles-zeros]
The poles-zeros tag has no usage guidance.
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1answer
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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 ...
2
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1answer
66 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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0answers
14 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, ...
5
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2answers
353 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 ...
5
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2answers
73 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
11 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 ...
3
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1answer
56 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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0answers
18 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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0answers
35 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 ...
0
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1answer
58 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 ...
2
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1answer
60 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
34 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 ...
0
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1answer
83 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?
0
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1answer
57 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 ...
1
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1answer
51 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/...
1
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1answer
74 views
Octave - freqz strange results
I wrote octave code to find transmittance based on zeros and poles:
...
0
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1answer
59 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' ...
0
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1answer
89 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?
1
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2answers
152 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 ...
1
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1answer
198 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 ...
0
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1answer
122 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 ...
1
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1answer
241 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
181 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
66 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$$\mathbb{R}$
How we can ...
0
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1answer
218 views
BIBO Stability for system with no poles
I have two questions regarding systems with no poles:
Why does a system with no poles have a finite support?
Why if the system has a finite support it means that it is BIBO
stable?
0
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1answer
62 views
What happens when the poles of this z-transform function are outside the ROC for a signal?
I am given a z-transform function for a signal $h[n]$. It's $H(z)=\frac{2z^2-0.75z}{(z-0.25)(z-0.5)}$. I am supposed to find $h[n]$ and check the stability of the system for these cases:
a)ROC: $|...
1
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2answers
290 views
How to find difference equation, given poles and zeros?
I'm given poles at ${1+i}$ and ${1-i}$, and zero at $0$.
I have to find the difference equation and find out whether the system is stable.
Now I found in a similar question, which structure I tried ...
1
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1answer
412 views
How to plot the poles and zeros of this Bandpass Filter in MATLAB?
So I'm trying to design a band pass filter in MATLAB (with a center frequency of 10kHz and a sampling frequency of 44kHz).
I have calculated the transfer function but I'm not sure how to enter this ...
2
votes
1answer
57 views
Find a stable transfer function $G(z)$ such that $|G(z)| = |H(z)|$
Consider the following causal IIR transfer function:
$$ H(z) = \frac{2z^3 - 4z^2 + 9}{(z-3)(z^2+z+0.5)} $$
Is $H(z)$ a stable function? If it is not stable, find a stable transfer function $G(z)...
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1answer
62 views
1
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1answer
71 views
Poles and zeros in time domain of analogs filters
I am currently studying two Butterworth and Chebyshev low-pass filters of order $n =3$ and $n=2$ respectively, whcih are in fact two prototypes to make a bandpass filter. The transfer function that I ...
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0answers
154 views
Simple Pole-Zero placement bandpass filter doesn't work in MATLAB
I'm trying to make a simple bandpass filter using Pole-Zero Placement method, which has unity gain at frequency w=0.37pi and 3 dB cutoff frequency wc=0.42pi (has a gain of 1/sqrt(2) at that frequency)....
0
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1answer
203 views
Pole zero plot, normalizing frequency response plot?
I'm asked to plot the frequency response (amplitude) given a specific pole-zero diagram.
$$ 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
108 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
98 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 ...
0
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1answer
156 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
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1answer
226 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:
$$
s = \frac{2}{T_d}*\frac{1-z^{-1}...
1
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1answer
99 views
Drawing the modulus from a Transfer function
As you may guess from my other questions i am a student so pardon me any ignorance and guide me to the truth. Thanks
In this exercise from an exam i was given that transfer function with poles and ...
0
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1answer
86 views
How to determine the poles from a graph
From my knowledge of stability, I understand that if the function approaches a finite number then the system will be stable. Thus if a system is stable its poles will be on the left of the $j\omega$-...
0
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1answer
471 views
Impulse response function from pole-zero graph
I know that that the poles of this system are: $s_1 = -1 + 2j$ and $s_2 = -1 - 2j$. I think to solve this problem I would need to find the laplace of this plot, with the formula:
$$
W(s) = \frac{\rm ...
3
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1answer
365 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
178 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 ...
0
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1answer
64 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
195 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
8k 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
116 views
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
756 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
372 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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58 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
377 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 ...
