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Questions tagged [poles-zeros]

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Methods to determine stability of open-loop systems

Which methods can be used to analyze the stability of open-loop systems only, closed-loop systems only, and both of them? As far as I understand, you can determine the stability of open-loop and ...
0 votes
0 answers
29 views

Need help with deriving a recursive formula for a control system optimization integral

I need some help with a problem that appears in one of the exercises of "Introduction to Stochastic Control Theory" by Karl J. Åström: Chapter 5, page 141, problem 8. It is about deriving a ...
2 votes
3 answers
309 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 transform which maps the $s$-...
1 vote
1 answer
78 views

Decay of the impulse response for poles contained in the unit circle

I've been struggling with the following exercise in Ljung's "System Identification: Theory for the User" (Problem 3G.1): Given a rational transfer function $G(z)$ such that its poles are all ...
0 votes
1 answer
251 views

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 ...
2 votes
0 answers
46 views

How to handle non-causality when decomposing a 4th order IIR filter into a parallel bank of second order filters?

What I am trying to do I am trying to code a Gaussian smoothing filter using the 4th order IIR filter described in Van Vliet's paper "Recursive Gaussian derivative filters". My code works ...
0 votes
1 answer
135 views

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 ...
3 votes
6 answers
3k 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 ?...
1 vote
2 answers
154 views

2 votes
2 answers
2k 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 ...
1 vote
2 answers
442 views

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 ...
2 votes
2 answers
261 views

How to determine number of poles or zeros in prony's method?

I would like to use Prony's method for signal modelling. I want to design a filter such that its impulse response is equal to the message signal. I use the function ...
0 votes
1 answer
48 views

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 $A_p(z)$ ...
1 vote
1 answer
175 views

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 ...
-1 votes
2 answers
92 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 ...
2 votes
1 answer
87 views

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 ...
4 votes
2 answers
1k views

1 vote
2 answers
216 views

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: ...
-1 votes
1 answer
667 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 (...
0 votes
1 answer
74 views

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 $Z$-...
0 votes
1 answer
555 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 ...
1 vote
1 answer
201 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 (...
1 vote
2 answers
61 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 ...
2 votes
2 answers
365 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 ...