Questions tagged [poles-zeros]
The poles-zeros tag has no usage guidance.
2
votes
1answer
55 views
Hidden zero in system equation $H(z)$
An FIR linear phase filter has unit sample response $h[n]$ that is real with $h[n]=0$ for $n < 0$ and $n > 7$. If $h[0]=1$ and the system function has a zero at $z=0.4e^{j\pi/3}$ and a zero at $...
1
vote
1answer
33 views
Does the system function H(z) for a filter always have symmetry above and below the real x-axis?
When I look at the Pole/Zero diagrams in the DSP books it appears that whatever
pole or zero is above the real x-axis from:
$$\omega=0 \rightarrow \pi$$
is always reflected as a mirror image ...
0
votes
1answer
45 views
Is the inverse of a causal system also causal?
If I have a causal system H(z) and I find the inverse of this system:
$$
G(z) = \frac{1}{H(z)}
$$
Is G(z) also causal?
0
votes
1answer
27 views
Get the discrete-time poles and zeros from continuous-time poles and zeros
How do you implement the following function:
$$[Z^d, P^d, K^d] = \text{fcn} \,(Z^c, P^c, K^c),$$
where $Z^c = [z^c_m, ..., z^c_1]$, $P^c = [p^c_m, ..., p^c_1]$, and $K^c$ are zeros, poles, and gain ...
1
vote
1answer
37 views
Determine poles and zeros of a specific filter design
I have a design question and need to determine poles-zeros of a IIR bandpass filter.
Requirements are:
1-order should be 3
2-causal
3-real valued impulse response
4-stable
5-cutoff freq: pi/3-pi/...
1
vote
1answer
60 views
Octave - freqz strange results
I wrote octave code to find transmittance based on zeros and poles:
...
0
votes
1answer
36 views
Determining asymptotic stability using transfer function?
In an exam task, I am asked to determine the transfer function of the following direct-time system and decide whether it's stable.
I think this system is canonical and the amplifiers 'on top' ...
0
votes
1answer
51 views
Trivial and non-trivial zeros
I am new to DSP, and I'm self studying. Could someone please explain to me what do we mean by trivial and non-trivial zeros?
1
vote
2answers
107 views
Stability of system with poles inside unit circle - conflict with differential equation
I am trying to understand why a system with a single pole inside the unit circle is stable. For example, take a system with one pole at $z=\frac{1}{2}$. The literature says the system is stable. As a ...
1
vote
1answer
89 views
How to determine poles and zeros of the z-transform?
This is a simple question, but I just don't understand how we determine the poles and zeros of a rational system function.
For example, for the LTI system described by this constant coefficient ...
0
votes
1answer
79 views
How can I determine the order of filter?
This is my first study about signal analysing. I'm very confused about filter order. My problem is how can I know whether its 12-th order, or 2nd order like the book says so? I already knew that slope ...
1
vote
1answer
197 views
IIR filter design fitting step response
I have access to the step response of a system and I want to find its poles and zeros without knowing the order of the system.
Consider an example of a step response of the system shown in the ...
0
votes
1answer
72 views
Poles and zeros map
Given the following map of poles and zeros for some $H^L(s)$:
How can I understand from the map that the given Transfer function is LPF?
Hence the poles are located at the hight frequencies it should ...
1
vote
1answer
44 views
Poles of the transfer function in Z Transform
Given that:
$H(z)$ has 4 poles maximum.
$H(z)$ has a pole at $z_1=a+bi$
Given that the impulse response $h[n]$ is:
Symmetric: $h[n] = h[-n]$
Real: $\forall$$n$ , $h[n]$$\in$$\mathbb{R}$
How we can ...
0
votes
1answer
149 views
BIBO Stability for system with no poles
I have two questions regarding systems with no poles:
Why does a system with no poles have a finite support?
Why if the system has a finite support it means that it is BIBO
stable?
0
votes
1answer
58 views
What happens when the poles of this z-transform function are outside the ROC for a signal?
I am given a z-transform function for a signal $h[n]$. It's $H(z)=\frac{2z^2-0.75z}{(z-0.25)(z-0.5)}$. I am supposed to find $h[n]$ and check the stability of the system for these cases:
a)ROC: $|...
1
vote
2answers
186 views
How to find difference equation, given poles and zeros?
I'm given poles at ${1+i}$ and ${1-i}$, and zero at $0$.
I have to find the difference equation and find out whether the system is stable.
Now I found in a similar question, which structure I tried ...
1
vote
1answer
313 views
How to plot the poles and zeros of this Bandpass Filter in MATLAB?
So I'm trying to design a band pass filter in MATLAB (with a center frequency of 10kHz and a sampling frequency of 44kHz).
I have calculated the transfer function but I'm not sure how to enter this ...
2
votes
1answer
57 views
Find a stable transfer function $G(z)$ such that $|G(z)| = |H(z)|$
Consider the following causal IIR transfer function:
$$ H(z) = \frac{2z^3 - 4z^2 + 9}{(z-3)(z^2+z+0.5)} $$
Is $H(z)$ a stable function? If it is not stable, find a stable transfer function $G(z)...
-1
votes
1answer
60 views
1
vote
1answer
65 views
Poles and zeros in time domain of analogs filters
I am currently studying two Butterworth and Chebyshev low-pass filters of order $n =3$ and $n=2$ respectively, whcih are in fact two prototypes to make a bandpass filter. The transfer function that I ...
0
votes
0answers
119 views
Simple Pole-Zero placement bandpass filter doesn't work in MATLAB
I'm trying to make a simple bandpass filter using Pole-Zero Placement method, which has unity gain at frequency w=0.37pi and 3 dB cutoff frequency wc=0.42pi (has a gain of 1/sqrt(2) at that frequency)....
0
votes
1answer
161 views
Pole zero plot, normalizing frequency response plot?
I'm asked to plot the frequency response (amplitude) given a specific pole-zero diagram.
$$ 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}) =...
1
vote
1answer
108 views
Design a filter which passes all frequencies except $\omega=\pm\frac{\pi}{2}$ and plot its pole-zero diagram
Also draw its normalized frequency response.
What is the ROC?
This has to be done in z-plane so there must be two poles at $+i$ and $-i$ since they cannot be included in region of convergence. Is my ...
1
vote
1answer
69 views
Question about poles and zeros in AR filter
For AR HP filter
zeros, to the right of the imaginary axis
poles outside the unit-circle
zeros on the real axis
poles, to the left of the imaginary axis
Apparently, the right answer ...
0
votes
1answer
123 views
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 ...
1
vote
1answer
185 views
Butterworth low pass filter zeros location after bilinear transformation explanation
I am studying in a text book the transformation of a continuous time Butterworth low pass filter into a discrete time filter by means of bilinear transformation:
$$
s = \frac{2}{T_d}*\frac{1-z^{-1}...
1
vote
1answer
79 views
Drawing the modulus from a Transfer function
As you may guess from my other questions i am a student so pardon me any ignorance and guide me to the truth. Thanks
In this exercise from an exam i was given that transfer function with poles and ...
0
votes
1answer
65 views
How to determine the poles from a graph
From my knowledge of stability, I understand that if the function approaches a finite number then the system will be stable. Thus if a system is stable its poles will be on the left of the $j\omega$-...
0
votes
1answer
394 views
Impulse response function from pole-zero graph
I know that that the poles of this system are: $s_1 = -1 + 2j$ and $s_2 = -1 - 2j$. I think to solve this problem I would need to find the laplace of this plot, with the formula:
$$
W(s) = \frac{\rm ...
3
votes
1answer
323 views
For a system to be causal, number of finite zeros <= number of finite poles. Why?
I read in this pdf that for a system to be causal, the number of finite zeros must be no greater than number of finite poles. Why?
I know that for a system to be causal, $h[n]=0$ for all $n<0$. ...
1
vote
2answers
171 views
What are poles and zeroes (with respect to the inputs and outputs of a system)?
I get it, about poles and zeroes, when we talk in terms of the transfer function.
But, if the transfer function is the ratio of the output to the input, then if the input signal is zero, then the ...
0
votes
1answer
60 views
Create an input so that poles show up as outputs?
Let's say we have a rational, causal, stable LTI system with transfer function
$$H(z) = \frac{A(z)}{B(z)}$$
If $H(z)$ has $N$ poles, we can in theory have only 1 of those poles, $p_i$, show up at the ...
1
vote
2answers
172 views
Invertibility of Room Impulse Response: Reproducing Research Paper
I have been trying to reproduce this paper¹. Few things which are unclear to me. The paper talks about finding whether a given Room Impulse Response(RIR) is invertible or not based on Nyquist plot.
...
4
votes
1answer
7k views
Position of poles and Stability in $z$ domain
We know in Laplace Transform, if the poles lie on the left of $j\omega$ axis, we can say the system is stable. Similarly can we comment on the stability based on poles position in $\mathcal Z$-...
1
vote
2answers
99 views
which filters are these?
Location of poles are given in unity circle and 4 zeros are given at origin for every plot,How to check which plot shows which filters?
For the Option (C) i am doing like this
I can write the ...
1
vote
1answer
672 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 ...
-2
votes
1answer
298 views
Why zeroes near the unit circle cause a dip in frequency response, while poles cause a peak?
I have an exam tomorrow and I really can't figure out the question in the title.
1
vote
0answers
45 views
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 ...
0
votes
1answer
334 views
Calculating poles with complex numbers and quadratic equation
given: $z^2 + 0.8 \sqrt2 z + 0.64 = 0 $
Then, I am using the quadratic equation:
$ z_{1,2} = \frac{-0.8 \sqrt2 \pm \sqrt{(0.8\sqrt2)^2-4 \cdot 0.64}}{2} $
Wolfram Alpha says it the end there should ...
0
votes
1answer
579 views
How to check if the poles of transfer function are stable?
$$H(z)=\frac{az}{[z-(b+ja)][z-(b-ja)]}$$
The two poles are looking like this:
$z_{\inf, 1}=b+ja, z_{\inf, 2}=b-ja$
I know they must be inside the unit circle: $|z_{\inf,i}|<1$
So I replace the ...
4
votes
2answers
1k views
Transposed Direct Form II VS Direct Form II IIR filters?
I read in "Discrete-Time Signal Processing" Reference, in transposed Direct Form II filters section, that it implements zeros first then poles(unlike Direct form II which implements poles first), ...
3
votes
2answers
103 views
Finite length truncated exponential sequence $\mathcal Z$-transform, zeros over circle explanation
I'm looking at an example on how to obtain the $\mathcal Z$-transform from a finite length truncated exponential sequence, namely:
$$x[n] =
\begin{cases}
a^N &\text{for} & 0 \leq n \leq N-1\\...
2
votes
2answers
1k views
Conjugate reciprocal pairs of zeros and poles in FIR design
Assuming the impulse response $h[n]$ of an FIR filter is real for all $n$,
Why are zeros and poles in FIR design found in reciprocal and conjugate pairs?
Is the assumption necessary for this ...
1
vote
1answer
5k views
Filter design with zero - pole placement method
I have some question for you about Filter design.
Α. Calculate the transfer function in order to stop the frequency of $300\textrm{ Hz}$ for sampling frequency at $12\textrm{ kHz}$. Use the
zero – ...
4
votes
1answer
2k views
Poles and zeros of a transfer function
What are the poles and zeros of this transfer function (in $z$):
$$H(z)=z+2+z^{-1}$$
and how would you approach the resolution of such problem?
Personally, I would write
$$H(z)=\displaystyle\frac{...
0
votes
2answers
758 views
A question about the meaning of pole in time domain
Lets say I have a transfer function $H(s)$ of a system defined in $s$-domain as:
$$H(s) = \frac{1}{s - (-1-j)}$$
So I conclude that the pole on the $s$-plane is where $s = 1+j$. So far so good.
Now ...
1
vote
1answer
354 views
How do I go from LPC coefficients to a filter polynomial?
I've recently begun experimenting with LPC, and while I understand that it works, I'm still slightly lost on why it works.
Specifically, I understand that LPC involves finding coefficients $a_1, a_2, ...
0
votes
1answer
144 views
Conjugate Pole Pairs
I am currently studying for an exam for a Speech Processing course I am taking and stumbled across this question in one of the sample exams:
I began to plot the pole-zero configuration placing my ...
0
votes
1answer
33 views
Pole-Zero Configuration of Glottal Signal
I am currently studying for an exam in my Speech Processing course this Friday and I stumbled upon this question in one of the sample exams:
The answer to this question was given as:
Can someone ...
