Questions tagged [poles-zeros]
The poles-zeros tag has no usage guidance.
196
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Z Transform and Difference Equation [closed]
Given that
$$H(Z) = 4z+2/(4z^2+2)*(2z-1).$$
Find the difference equation of g(n) such that g(n) and h(n) are two cascading filter such that output is same as input. Moreover find the frequency ...
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52
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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
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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 ...
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3
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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 ...
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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, ...
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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 ...
- 295
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2
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39
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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 ...
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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 ...
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0
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63
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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 ...
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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 ...
- 115
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2
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507
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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 ...
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1
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240
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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 ...
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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 ...
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2
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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
$$\frac{3(1+\frac{2}{...
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Significance of poles in a Transfer Function
Sorry for asking this basic question, but I am new to signal processing and have this doubt for a long time.
I have been studying signal modelling and have
$$H(z) = B_q(z)/A_p(z)$$
where $A_p(z)$ ...
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2
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339
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LPF design with pole/zero placement at rejection at specified freq
I am about to design a low-pass filter with a zero/pole placement method in such a way that rejected frequencies are placed at $500\,\text{Hz}$ and their multiples.
Are there any simple instructions ...
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finding x[0] from the region of convergence
I have the ROC of a signal $x[n]$ with $z$-transform $X(z)$ as below:
Now I am wondering how I can find $x[0]$ by not calculating inverse z transform based on the roc, I am looking for a simpler, and ...
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1
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Confusions regarding expressions of transfer functions of ideal integrator and ideal differentiator?
The ideal integrator has differentiator has transfer function H(s)= -1/RCs while ideal differentiator has transfer function H(s)= -RCs
It is often said regarding above integrator that it has a zero at ...
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1
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63
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How does the phase/gain margin method work?
We have the closed loop transfer function:
$$T(s)=\frac{L(s)}{1+L(s)}$$
So as far as I understand we check along the $j\omega$-axis on the Bode plot whether $L(s)=-1$, cause that's when $T(s)$ has ...
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2
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Poles and zeros form of a transfer function
I know that a transfer function for a discrete-time LTI system can be written in the form
$$
H(z) = \frac{Y(z)}{X(z)} = \frac
{ \displaystyle\sum_{m=0}^M {b_m z^{-m}}}
{1 + \displaystyle\sum_{n=1}^...
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2
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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 (...
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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 ...
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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 ...
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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 ...
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2
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181
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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:
...
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1
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74
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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 $Z$-...
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138
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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 (...
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380
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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 ...
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142
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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 ...
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2
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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 ...
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2
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261
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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 ...
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3
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168
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How can you see from the transfer function of a system that it has feed forward/feedback elements?
Furthermore, how can you see from the pole/zero plot if the system has feed forward/feedback elements?
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ROC of $\mathcal{Z}$-Transform and zeros
Theorem: Let $$f(z) = \sum_{n=0}^{+\infty}a_nz^n$$ where $z\in\mathbb{C}$.
If $f(z_0)$ exists for some $z_0\in\mathbb{C}$ then it converges for all $z\in\mathbb{C}$ such that $|z|\lt|z_0|$.
Proof: It ...
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1
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279
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Understanding the Chebyshev2 Bandpass Filter Poles-Zeros Plot
EDIT
This ended up being a bug with my plotting code :)
I'm relatively new to using IIR filters, I wanted a bandpass filter for the 0.5Hz -> 5.0Hz frequency range and was looking at the zero-pole ...
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1
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58
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How to convert passband and stopband frequencies to poles and zeros
I have a NI 9229 digitizer with the following datasheet.
The datasheet mentions:
a passband frequency of $0.453f_s$ with a flatness of $\le0.1\,\text{dB}$
a stopband frequency of $0.547f_s$ with ...
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33
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Zeroes and poles for a system
I have run into some issues on an exercise for the course in signal analysis and systems I am currently studying.
We are to create an echo effect and are using the system below:
I am to find the ...
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1
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How to identify from poles and zeros if it is a bandpass
For an example, this is a figure I made from MATLAB, based on the poles and zeros, how can identify if it is a bandpass filter.
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254
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Complex damped exponential signal with repetitive poles and the significance of falling factorial
I was modelling a complex damped exponential signal (discrete) with unique poles as below:
\begin{equation}
x = \sum_{k=1}^{K} (a_k e^{(j\phi_k)})(e^{\{(j2\pi f_k - \alpha_k)\Delta t\}t}), \quad t ...
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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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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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1
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1k
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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 ...
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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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520
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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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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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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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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 $s$-...
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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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2
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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 ...
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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 ...
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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 ...
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