# Questions tagged [poles-zeros]

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### How poles are related to frequency response

I have recently fallen into fallacy, considering pole s=1 as there is infinite response at frequency 1. Yet, response was only 1. Now, can you derive the frequency response, given the poles? ...
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### What are poles and zeros?

The concept of poles and zeros in filters was introduced to me during our lab (our lab isn't sync with our lecture) through the pole-zero plot generation of filters in MATLAB. I didn't get its ...
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### What is the difference between natural response and zero input response?

I am new to DSP and was going through different responses of a system subjected to an input. My understanding of zero input response is: it is the response/output of the system when the input signal ...
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### Nyquist plot interpretation when curve hits the origin

I'm a bit confused about the interpretation of the Nyquist plot when the origin is part of the plot. In this case I'm not even considering closed loops, I'm just looking at the Nyquist Plot of a given ...
• 193
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### 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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### What is the relationship between poles and system stability?

I see two notions that describe the relationship between poles and system stability. But they are not the same from my understanding The system is BIBO stable if and only if all the poles are in the ...
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### 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 – ...
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### 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), ...
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### Pole Quantization Patterns in 2nd Order IIR Resonators

Background My typical approach to fixed point design for digital filters is to iteratively scale and increase quantization while comparing the fixed point simulation to the floating point design ...
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### Why don't unit circle poles lead to infinite amplitude response for Butterworth lowpass?

This is probably a very stupid question. In many places (e.g. here), the Butterworth filters, e.g. lowpass, are described as being "allpole" filters, that have all of these poles on the unit ...
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### Pole-zeros of a real-valued causal FIR system

Could someone please help me with the following question? Below is the magnitude response of a real-valued causal linear phase FIR system of order N = 6. Determine the location of poles and zeros. I ...
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### Identifying the magnitude and impulse response from pole zero plot quickly

I have an exam next week and it's verty certain that a task of this kind will be there. Are there some good tips how to match the right pole zero plot to the right responses? No proof is needed in ...
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### How to determine if a filter is bandpass/stopband from its pole-zero diagram in z-domain

How can we determine if a filter is bandpass or stopband, just by looking at its pole-zero diagram in z-domain? For exmaple, if we have a system with third-order pole at the origin and a zero on the ...
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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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### Are all IIR filters unstable in nature?

I know this question has been asked here numerous times. But I am still unclear here :( My book says, A linear time-invariant system is stable if its impulse response is absolutely summable. (G. ...
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### Is this system causal or not?

My efforts of solving this question are below. I came to a conclusion that this system is causal, since: $$\begin{cases} w[k]+5w[k-1]+6w[k-2]=x[k] \\ y[k]=w[k]+2w[k-1]+3w[k-2]+4w[k-3] \end{cases}$$...
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### 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 ...
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### How does one calculate a pole-zero plot?

To my understanding, pole-zero plots are used to analyze or visualize transfer functions. Suppose there is some very simple system, for example a simple low-pass filter (so it is linear and time-...
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### What is the reason behind complex conjugate pairs in Linear Phase FIR filter analysis from the Pole Zero plot

When we say that a Generalized Linear Phase System must satisfy the pole zero plot with the condition that a complex zero not on the unit circle exist's in a pair of 4. Then I understand that I need ...
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### Laplace Transform: zeros and corresponding impulse response $h(t)$

Poles and the impulse response If our impulse response is in the form : $$h(t) = e^{-\sigma_0 t}\cos(\omega_0 t) \, u(t)$$ (where $u(t)$ is the unit step function) And its Laplace transform is : H(s)...
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### Plane Settings of the Matched $z$-transform Method
I've come across that the matched $z$-transform maps poles of the $s$-plane design to locations in the $z$-plane. My question is, what is the $s$-plane and what does this mean? I'm aware that the ...