# 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.

379 questions
Filter by
Sorted by
Tagged with
221 views

### Changing limit of integral make time-variant to time-Invariant system

$S_1:x(t)\longrightarrow y(t) = \int_{-\infty}^{3t}{x(\tau)\,d\tau}$ $x(t-t_0)\longrightarrow y_1(t) = \int_{-\infty}^{3t}{x(\tau-t_0)\,d\tau}$ $= \int_{-\infty}^{3t-t_0}{x(z)dz} \neq y(t-t_0)$ ...
695 views

### Linearity, Causality and Stability of a System

Consider a system: $$y[n] = y[n-1] + u[n],$$ where $y[n]$ is the output and $u[n]$ is the unit step function. Is this system causal, linear, time-invariant and stable ? My attempt at the ...
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 ...
441 views

62 views

### Linear Systems, Sparse Solutions, and $4 \times 4$ Sudoku Algorithm [closed]

I am unable to understand the paper Linear Systems, Sparse Solutions, and Sudoku. I have to form a $4 \times 4$ Sudoku using the algorithm in this paper. Can somebody please provide me the algorithm ...
119 views

Give the equation $$y[n]-y[n-1] +\frac14y[n-2]= x[n]$$ With initial conditions $$y[0]=0\\ y[1]= 0$$ Find the step response. I have been able to get the solution $$y[n] =C_1(\frac12)^n +C_2(\frac12)^... 1answer 330 views ### Steady State of a Difference Equation using MATLAB I'm given this difference equation, and I'm being asked to plot its response to an input x[n] = 4\sin^3\left(0.25\pi n+\frac \pi 3\right)u(n):$$ y(n) = 0.9051y(n-1)-0.598y(n-2)+0.29y(n-3)-0.1958y(...
Consider I can find the step response of a system with the following method: We can easily find the step input of a system from its transfer function. Given a system with input $x(t)$, output $y(t)$ ...