# 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.

406 questions
Filter by
Sorted by
Tagged with
97 views

### is y[n] = x[n] + n time invariant?

My steps were as follows: $\ x_2[n] = x[n-k]$ $\ y[n-k] = x[n-k] + (n-k)$ and $\ y_2[n] = x_2[n] + n = x[n-k]+(n-k)$ Does this mean that it is indeed time invariant?
21 views

34 views

### Is $y(t) = \cos(t) + x(t)$ a time-invariant system?

Is $y(t) = \cos(t) + x(t)$ a time-invariant system? $y(t-k) = \cos(t-k) + x(t-k)$ But it isn't equal to $\cos(t) + x(t-k)$ So, would it be time-invariant?
1k views

### Are all LTI systems invertible? If not, what is a good counterexample?

I have been trying to figure this out for a while now. Everywhere I have looked I could easily find examples of invertible LTI systems, but I could not find any counterexamples. Can anybody shed some ...
219 views

### I somehow “proved” that given any LTI system, its transfer function has to be constant. What am I missing?

A transfer function is defined as the Laplace transform of the ratio of output to input. Also, every LTI system has an eigenfunction. Given such eigenfunction as an input, the ratio of the output to ...