# Questions tagged [poles-zeros]

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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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1 vote
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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 ...
1 vote
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### 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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### 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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### 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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### 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?
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 ...
65 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....
62 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 ...
95 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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### 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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### 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 ...
115 views

### Is it a mandatory condition that complex poles and zeros should always exist as conjugate pairs?

Complex poles and zeros always exist in conjugate pairs?If not always, in which context applicable? https://www.informit.com/articles/article.aspx?p=32090&seqNum=9 The above link mentions related ...
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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 ...