State the Causality, Stability, Commutative and Distributive Properties of LTI systems.

 Causality Property: 

        A system is said to be a causal if its output at anytime depends upon present and past inputs only. A system is said to be non-causal system if its output depends upon  future inputs also. 

Example:         y(t) = 5.x(t) ; Causal System 

                        y(t) = 5.x(2t) ; Non Causal System 

Stability Property: 

        When the system produces bounded output for bounded input, then the system is called bounded input, bounded output stable. A system which does not satisfy the above condition is called a unstable system. 

Example:         y(t) = x(2t) ; Stable System 

                        y(t) = t.x(t) ;Unstable System 

Commutative Property: 

        The commutative property means simply that x convolved with h is identical with h convolved with x. The consequence of this property for LTI systems is that for a system with a specified input and impulse response, the output will be the same if the roles of the input and impulse response are interchanged.

                                x(t)*h(t)= h(t)*x(t) 

Distributive property: 

   According to this property, if the same input is two systems in parallel then the input can convolve with the combination as well as each system individually. The result of both operations will be equal.

                        x1(t)* {x2(t)+x3(t)}= x1(t)*x2(t)+ x1(t)*x3(t)