# Questions tagged [linear-systems]

A linear system operates on inputs with only linear operators so the response to a complex input can be analysed as the sum of the response to a set of simpler inputs. This mathematical property makes the analysis of linear systems much simpler than non-linear systems where this summation or superposition does not hold. Linear systems are generally further classified as time invariant, meaning that there characteristics do not change over time.

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### Analog LTI system impulse response

I have the following question in my mock exam! My Answer: I can apply the dirac delta to know the impulse response. Or use the transfer function $H(z) = \frac{Y(z)}{X(z)}$. I am not sure about the ...
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### Slope of phase function

Would appreciate some help understanding if I take the phase function of some transfer function and derivative it in the linear part of it which is around the resonant frequency what does this slope ...
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### How to find a system without an input $x[n]$ is linear or non linear

The question is this: $$y[n] = \cos\left(\frac{5\pi}{8}n + \frac{\pi}{4}\right)$$ This is what my teacher said when I asked him for help-: In any system, inputs are not given, then we have to assume ...
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### Why aren't the integrator and the differentiator inverse systems?

I have a statement that leads to a paradox, but I'm incapable of finding the part where I'm wrong. The integrator system $$x(t) \mapsto y(t)=\int_{-\infty}^{t}{x(\tau) \, {\rm d} \tau}$$ is a linear ...
1 vote
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### How to update point spread function of blind deconbolution by conjugate gradient?

There is an unblurred image $g$ and a blurred image $x$. Their relationship is expressed by the following formula using $psf$(point spread fucntion, size is $5×5$ kernel). $g = x \otimes psf\tag 1$ ...
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### What is the importance of obtaining a linear signal?

I am a computer scientist who has started doing some work in the electrical engineering space – in particular, photonics. While reading about interferometric systems, I have noticed that there seems ...
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### Identify out signal from in signal and impulse response

Hi there I am studying a course in signal processing and systems. I was given an excecise which I am having a great deal of trouble solving. I am allowed to solved using matlab, but for top marks I ...
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### Definition of frequency response

I studied various signal processing materials for a long time, and I have a question. Considering an LTI filter, one can define its frequency response by evaluating its transfer function $H(z)$ on the ...
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### Mixing Kalman filter and least-squares

I'm not sure it is the right department. I try my chance I am wondering if there is a way to make a hybrid formulation of a least-square problem and a Kalman filter. Let me explain what I mean: The (...
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### How to prove that this system is an invertible system or not?

How could i go throw proving that this system $y(t)=\int_{-\infty}^{t}e^{-(t-\tau)}x(\tau)d\tau$ is invertible system or not ?
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### Linear system stability criteria

Suppose we have a closed-loop system $H(s)=\frac{A(s)}{1+A(s)f(s)}=\frac{A(s)}{1+T(s)}$. I've seen the stability of the system stated a couple ways: If $H(s)$ has any poles in the RHP, then it is ...
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### When is a LTI IIR $H(z)$ system minimum phase

EDIT: I failed to mention that the system's inverse also needs to be causal and stable. I cannot wrap my mind around on how when a system and its inverse are both causal and stable and LTI IIR it is ...
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### Signal separation

This is probably a blind signal separation problem of sorts, but it seems like it should be easier than I am finding it. Let’s say I have N time series, each of length [M x 1] that are a superposition ...
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