# 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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### How to evaluate performance of an ARMA, MA or AR model?

How to evaluate performance of a model after estimating ARMA/MA/AR parameters for any process x(n)? How to regenerate back a process after estimating average parameters? what kind of performance ...
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### How do I show if this system is time-varying? [closed]

$\displaystyle y(t) = x(t), t \ge 0$ and $-x(t), t \lt 0$ I can anticipate this system is time-varying. However, I cannot be sure it and prove it. please help me.
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### Is the system $L\{f[m,n]\}= c[m,n] f[m,n]$ shift invariant?

$c[m,n]$ is the spatially varying gain. My prof says that its not shift invariant. However if we put $m=m-k$ and $n=n-l$ we get $c[m-k,n-l] f[m-k,n-l]$ which is how a shift invariant system should ...
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### Discrepancy when calculating LTI system output using inverse z-Transform

I'm given a difference equation, $y[n]-0.4y[n-1]=x[n]$, and asked to find the natural response $y_n[n]$, forced response $y_f[n]$ and complete response $y[n]$ if $x[n]=4 (0.25)^nu[n]$ and $y[0]=0$. ...
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### BIBO stability and input at system's pole

My understanding of BIBO stability is that if a bounded input is applied to a discrete-time, linear, time-invariant BIBO system, the output will also be bounded. A sufficient condition for this is ...