# 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.

45 questions
Filter by
Sorted by
Tagged with
177k views

### What is meant by a system's “impulse response” and “frequency response?”

Can anyone state the difference between frequency response and impulse response in simple English?
5k views

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

I am new to DSP and was going through different responses of a system subjected to an input. My understanding of zero input response is: it is the response/output of the system when the input signal ...
2k views

### Do Causal Discrete-time systems have proper transfer functions?

In the case of continuous-time systems, if the system is causal, its Laplace transfer function is strictly proper (the degree of the numerator is less than the degree of the denominator). Is this ...
3k views

### Initial conditions for the LTI systems described as a difference equations

Why do we need the initial conditions to be zero for the LTI systems described as a difference equations? First question is why do we need it for linearity? I can't think of any example of the non ...
2k views

### Are complex exponentials the only eigenfunctions of LTI systems?

Is there an example of an eigenfunction of a linear time invariant (LTI) system that is not a complex exponential? Justin Romberg's Eigenfunctions of LTI Systems says such eigenfuctions do exist, but ...
435 views

### Is this system linear?

I have this system: $$y[n] = -\frac{1}{2} x[n+2] - y[n+1]$$ I have no idea how to prove if the system is linear or not, because, it depends on future outputs... Thanks for the help
227 views

### Output of a discrete-time LTI system different form than input?

This question is related to this one. I'm going through old exams for a 2nd year systems and transforms course, and came across this question. I'm posting this question just in case my other question ...
946 views

377 views

### Does instability make an otherwise LTI system nonlinear (or time-variant)?

I am spinning this question off from the question from johnny. Matt L. and I have had directly opposite conclusions to johnny's question. I want to decouple the question from issues of causality and ...
3k views

### Given the input and the output, how to determine the impulse response?

I would like to find the impulse response, $h[n]$, of an LTI system given the input $$x[n] = [1,-3,2]$$ and the output $$y[n] = [1,-1,-4,4]$$ I know that $y[t]=x[t]*h[t]$, but I am having hard ...
442 views

### A system that perfoms Fourier Transform operation - is it an LTI system?

If a system takes input as the time domain signal and outputs the frequency domain signal, is such a system an LTI system? For if the input time domain signal can be represented as a linear ...
2k views

### Why unit impulse function is used to find impulse response of an LTI system?

Hello i am working in digital image restoration field, recently i have studied concept of convolution, i studied that to find the impulse response/point-spread function of an LTI system, an unit ...
161 views

159 views

### should this be viewed as an impulse response or step response

I'm trying to teach myself the relation between simple discrete ODE's and the impulse response-step response concept. Getting back to the question: I don't expect anyone to read the whole thing but I'...