Questions tagged [poles-zeros]

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27 views

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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41 views

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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1answer
54 views

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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2answers
48 views

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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2answers
105 views

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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3answers
31 views

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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1answer
79 views

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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1answer
53 views

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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1answer
31 views

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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1answer
27 views

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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1answer
31 views

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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1answer
227 views

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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1answer
29 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
34 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
270 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 ...
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1answer
96 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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175 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
1k 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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56 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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46 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 ...
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0answers
68 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
42 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 ...
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1answer
269 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
169 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 ...
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1answer
44 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
78 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 ...
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1answer
79 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 ...
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2answers
170 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 ...
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2answers
138 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
115 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
71 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 ...
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1answer
46 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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21 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 ...
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1answer
50 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
53 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
83 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 ...
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2answers
962 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
111 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 ...
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38 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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166 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 ...
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1answer
154 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
66 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 ...
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5answers
912 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 ?...
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2answers
476 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{-...
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1answer
402 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 ...
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3answers
363 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 ...
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3answers
805 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 ...
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1answer
50 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{...
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1answer
146 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 ...
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1answer
119 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 ...