3.4.1 Mathematical representation of linear systems uThe input-output relationship of a linear system d n-1 ∴+a d dx(t (3.3) m-1 +…+b +box() where x(t=input of the system y(t=output of the system an, al, ao, and bm, b1, bo are systems parameters Ua linear constant-coefficient system or linear time-invariant(LTD) system: the parameters are constants❑The input-output relationship of a linear system: where x(t)= input of the system y(t)= output of the system an , a1 , a0 , and bm, b1 , b0 are system’s parameters. ❑A linear constant-coefficient system or linear time-invariant (LTI) system: the parameters are constants. 3.4.1 Mathematical representation of linear systems ( ) ( ) ( ) ( ) ( ) ( ) ( ) b x(t) dt dx t b dt d x t b dt d x t b a y t dt dy t a dt d y t a dt d y t a m m m m m m n n n n n n 1 0 1 1 1 1 0 1 1 1 = + + + + + + + + − − − − − −   (3.3)