# Tag Info

Accepted

### If the convolution of two signals is a unit impulse, what does this tell us?

It tells us that the systems are inverses of each other. The DFT of $$h_1[n]*h_2[n]= \delta[n]$$ is $$H_1[k] \cdot H_2[k] = 1$$ so we get $$H_2[k] = \frac{1}{H_1[k]}, H_1[k] = \frac{1}{H_2[k]}$$ In ...
• 44k
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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 ...
• 28.1k
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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....
• 50.2k
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### why exponential term neglected in equation?

The magnitude of that complex exponential is 1. Recall from complex algebra: any complex number can be expressed as $z = r e^{j \phi}$ where $|z|=r$ is its magnitude and $\arg z = \phi$ is the ...
• 4,124
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### Stability of system with poles inside unit circle - conflict with differential equation

What you are missing is that this is about a discrete-time system, because we're talking about poles and zeros in the complex $z$-plane and about poles inside or outside the unit circle. So there is ...
• 89.5k

### Why can adaptive IIR filters result in unstable solutions?

Although what @Fat32 wrote is correct, I think the potential instability of IIR filters is not the main reason for the instability of an adaptive IIR filter. After all, we can calculate the poles in ...
• 321
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### Allan Variance vs Autocorrelation - Advantages

My current work involves the design details of atomic clocks where we use the Allan Variance and Allan Deviation (ADEV) extensively. The primary point is that it can be used for non-stationary ...
• 50.2k
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### causality of the system $y[n] = x(2n)$

No it does not satisfy the condition. Simply take an example: $$n = 1 \implies y[1] = x[2]$$ Hence the output value at the present time $n=1$ depends on a future value of the input at time $n=2$. ...
• 28.1k
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• 89.5k
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### Stability of a system

For BIBO stability in the case of discrete time, there is a necessary and sufficient condition given by $\sum |h[n]| < \infty$ that is if the impulse response is absolute summable then the system ...
• 151

• 20.3k

### Definition of minimum-phase system

one thing about a non-minimum phase system (with a rational transfer function), is that it can be thought of as the series concatenation (or cascade) of a minimum-phase system, having identical ...
It is generally not true that the relation $Y(\omega)=X(\omega)H(\omega)$ is independent of the system's stability. For systems with a rational transfer function (i.e., systems that can be described ...