Questions tagged [poles-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, ...
DaveC's user avatar
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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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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 $s$-...
shampar's user avatar
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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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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 ...
Estacionario's user avatar
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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 ...
Vinícius Lopes Simões's user avatar
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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 ...
user102569's user avatar
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Relation of roots of a polynomial to amplitude distribution of its coefficients

Consider $g(x)=\sum_{k=0}^{p}a_kx^{k}$, and let $\{\tau_1,\tau_2,\cdots,\tau_p\}\in\mathbb{C}$ be the roots of $g(x)$. What is the relation between how $\{a_0,a_1,\cdots,a_p\}$ are distributed (in ...
Neeks's user avatar
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Inverse z transform - Pair of complex conjugate poles

How can I perform the inverse z-transform on the following $H(z)$ to be able to calculate a real-valued impulse response $h[n]$? $$ H(z)=\frac{z^2}{z^2+0.8\sqrt{2}z+0.64} $$ My idea was to find an ...
MisterFilter's user avatar
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What is damping ratio and natural frequency of z-domain with real negative pole and undifine region

As ilustrated in controlsystemsacademy shown relation between z-domain and s-damain poles by this image. with contour for natural frequency and damping ratio given by these equations. However there ...
M lab's user avatar
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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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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 ...
Volpina's user avatar
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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 ...
Il De Santa's user avatar
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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 ...
Rima's user avatar
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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-...
shampar's user avatar
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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 ...
Arkadiusz's user avatar
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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 ...
dsp_guy2020's user avatar
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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 ...
OscarArcila's user avatar
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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 ...
Gary Hand's user avatar
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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?
4charwon's user avatar
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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 ...
shampar's user avatar
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Calculating poles/zeros from 4+ order transfer function

I need to calculate the poles and zeros from minimum 4th order (max ~20) filter coefficients. I have limitations that prohibit the companion matrix/eigen decomposition method used by roots() in Matlab....
kippertoffee's user avatar
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2 answers
91 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 ...
shampar's user avatar
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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 ...
shampar's user avatar
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1 answer
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What do poles do for a filter?

What are the disadvantages of having too many poles? Thanks.
IPython's user avatar
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1 answer
676 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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1 answer
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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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