Question

Question (1) ls the system S, given by (6 Marka y(t) = 3x(t-1)-2 a) Memoryless?
Memory less ?

Causal ?

Bounded input bounded output stable ?

Is the system invertible ?

Linear ?

Time invariant?

Answer 1

Y (t) = 3x (t - 1) - 2 a) memory less (or) static ? No The given system is not memory less. Memory less - present output depends only on present input then if is said to be memory less but in the given system present output depends on future value hence it is dynamic system. b) Causal ? No given system is non causal. Present output depends future value of the input hence it is non causal c) Bounded input bounded output stable? Phi es let consider input x (t) is a unit step function y (t) = 3 u (t - 1) -2 output always sounded hence stable d) invertible ? No it is non inventible input can not be relavered from O/P d) linear? No y (t) = 3x (t - 1) -2 y_1 (t) = 3x_1 (t - 1) - 2 y_2 (t) = 3x_2 (t - 1) - 2 y_3 (t) = 3 [x_1 (t - 1) + x_2 (t - 1)] -2