Please help ### Analysis of a Discrete Signal**Problem Statement:**A discrete signal is described by the equation:\[ T(x(n)) = n \times x(n) \]You are required to check the following properties of the signal:- **Linearity:** Determine if the system is linear by checking if it satisfies both additivity and homogeneity.- **Memory:** Evaluate if the system is memoryless or if it depends on past or future input values.- **Time Invariance:** Assess if the system's behavior is consistent over time and does not change when shifted in time.- **Causality:** Check if the system is causal, meaning the output at any time depends only on present and past inputs and not on future inputs.

Given y(n) = T{x(n)} = n x(n) Need to find this output system y(n) is linear, causal, memory and time invariant or not.Linearity: A system is said to be linear if it obeys linear superposition Principle that is T[ax1(n)+bx2(n)] = a T{x1(n)} + b T{x2(n)}Given T{x(n) }= nx(n) = y(n)T{x1(n)} = nx1(n) and T{x2(n)} Let Input be x(n) = ax1(n) + bx2(n) , for this output should be y(n) = ay1(n) + by2(n) then we can say it as linear.y(n) = a T{x1(n)} + b T{x2(n)} y(n) = a n x1(n) + b nx2(n) = ay1(n) + by2(n) So given system is linear.Memory: Memory systems are also known as dynamic systems. A system is said to be Memory or dynamic if output depends on present and past inputs only not on future inputs. Here y(n) = n x(n). x(n) is present input.So y(n) is causal as it is not having future inputs. Time invariant: A system is said to be time invariant if output is independent of n or in other wordsy(n -n0) = x(n- n0). If input shifts by n0 then output also should shift by same n0. Here y(n) = n x(n) ----dependent on ny(n-n0) = (n-n0) x(n-n0) ---shift is not same. So y(n) is time variant. Causality: A System is said to be causal if output depends on only present inputs but not past and future inputs. y(n) = n x(n)Here x(n) is present input, it is not dependent on future & past . So y(n) is causal.Given system is linear, causal, memory and time variant.