ECEN221-LAB 2 Report Submission LAB Report 2 submission need to include both theoretical proof of linearity and time invariance plus your MATLAB simulation codes, all results including figures and discussions for the four systems as given in lab2systems MATLAB function. The following table need to be completed. The Table is filled for System 1 to help you for example purposes. Theoretical Proof for Linearity & Time Invariance (for System 1) is also given below the Table. 1. Table: Identifying Linearity & Time Invariance of Systems Table: Identifying Linearity & Time Invariance of Systems System No Input-Output Mathematical Linearity Time Invariance Relation (Equation) y(t)= x(t)u(t) Yes No 1. 2. 3. 4. 2. Example: Theoretical Proof for Linearity & Time Invariance for System 1: System 1: y(t) = x(t)u(t) a) Linearity Proof: sem 1 X(t) xz(t) y, (t) = x(t)u(t) > yz (1) = x2(t)u(t) Let 3(t) = ax(t)+bxz(t), then y; (t) = x; ()u(t) = (ax, (t) + bx,())u(t) = ax (1)u(t) + bx, (t )u(t) = ay()+by, (1) Since, yz(t)=ay(t)+byz(t), the system is linear. b) Time Invaraince if (t) For time invariance to hold for the sytem, y(t) = x(1)u(1) system y(t-1) = x(t-1, Ju(1-1) then tt-t.) Proof: Let xi(t) = x(t-to), then yi(t)= x; (1)u(t) = x(t-1 ult) Clearly y(t) = y(t-to), therefore the system is not time-invariant or it is time variant. 3. MATLAB Test Signals for Linearity t=[-2:0.005:10]; xl=(t>=0&t=-1&t=0&t=-1.5&t yz (1) = x2(t)u(t) Let 3(t) = ax(t)+bxz(t), then y; (t) = x; ()u(t) = (ax, (t) + bx,())u(t) = ax (1)u(t) + bx, (t )u(t) = ay()+by, (1) Since, yz(t)=ay(t)+byz(t), the system is linear. b) Time Invaraince if (t) For time invariance to hold for the sytem, y(t) = x(1)u(1) system y(t-1) = x(t-1, Ju(1-1) then tt-t.) Proof: Let xi(t) = x(t-to), then yi(t)= x; (1)u(t) = x(t-1 ult) Clearly y(t) = y(t-to), therefore the system is not time-invariant or it is time variant. 3. MATLAB Test Signals for Linearity t=[-2:0.005:10]; xl=(t>=0&t=-1&t=0&t=-1.5&t