# Tag Info

Accepted

### What is the difference between natural response and zero input response?

First it's important to realize that many authors use the terms zero-input response and natural response as synonyms. This convention is used in the corresponding wikipedia article, and for instance ...
• 79.2k
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### Who first understood the importance of poles?

If you consider poles of an integral transform domain to be important to the solution of differential equations: (as usual,) Euler did it first, 1753. One "importance" of poles is that they're part of ...
• 25.7k
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### Are all IIR filters unstable in nature?

Note that for stable IIR filters, the impulse response does approach zero as $n$ goes to infinity. It just never becomes exactly zero. However, the sum of the absolute values is finite. Just as an ...
• 79.2k
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### Position of poles and Stability in $z$ domain

Short Answer: All the poles of a causal (right-sided) and stable LTI system must be inside the unit circle whereas all the poles of an acausal (left-sided) and stable LTI system must be outside the ...
• 26.5k
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### Pole-zeros of a real-valued causal FIR system

Note the difference between the zeros at $0.3 \pi$ and at $0.8 \pi$. The first one is clearly a zero crossing, much like $abs(x)$ at $x=0$. At $\theta = 0.8 \pi$, however, the curve is tangent to ...
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### What is the relationship between poles and system stability?

I agree with Peter K.'s answer, but I would like to add one important point: the two statements in the question are only true for causal systems. The most general statement about stability for LTI ...
• 79.2k
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### What are poles and zeros?

Take the equation b/(x-c) with b non-zero. The ratio goes to infinity as x approaches c. So c is the location of a pole (something tall and pointy in a graph). Take the equation (x-b)/c with c non-...
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• 654
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### Why don't unit circle poles lead to infinite amplitude response for Butterworth lowpass?

You've made an understandable mistake. You are probably looking at this picture: That is not the unit circle, and it isn't even in the $z$ domain. What you are looking at is the locations of the ...
• 8,071
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### Nyquist plot interpretation when curve hits the origin

First to clear up the OP's misunderstanding: the Nyquist Stability Criteria involves clockwise encirclements of -1, not the origin, and this would be the polar plot for the open-loop gain specifically....
• 36.1k
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### Is it possible to know the order of the filter, just looking on the pole zero plot?

Count the number of poles and zeros; if the numbers aren't the same then the larger number is the filter order. Don't forget to count multiple poles or zeros with their multiplicity. Actually, you ...
• 79.2k
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### What's the Q of a pole at the origin of the s-plane?

Note that the formula given in your question is valid for a system with a complex-conjugate pole pair $p$ and $p^*$ with $\text{Re}(p)\neq 0$. As you've correctly pointed out, if for $|p|>0$ the ...
• 79.2k
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### A few conceptual questions about filter, pole, and bilinear

The poles of low pass and high pass Butterworth filters are indeed the same if both filters have the same cut-off frequency. The difference between the two lies in the numerator. A low pass filter has ...
• 79.2k