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Questions tagged [poles-zeros]

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2
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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
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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
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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
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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
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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
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1answer
60 views

Octave - freqz strange results

I wrote octave code to find transmittance based on zeros and poles: ...
0
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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1answer
60 views

What do poles do for a filter?

What are the disadvantages of having too many poles? Thanks.
1
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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 ...
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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 $\mathcal Z$-...
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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 ...
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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
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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
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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 ...