3.4.2 Representation of system 's characteristics in terms of transfer function or frequency response If all the systems initial conditions are zero, making Laplace transform of Eg (3.3) gives then the expression y(slans"+amS+.+a,s+ao X((bns"+bnsm+…+b1s+b。) The transfer function H(s) y(s)bm5+bm-ISm-++b,5+b H 1 (3.12) )as"+as 十a1S+a 0 The transfer function H(s) represents the transfer characteristics of a systemIf all the system’s initial conditions are zero, making Laplace transform of Eq. (3.3) gives then the expression The transfer function H(s): ❖The transfer function H(s) represents the transfer characteristics of a system. 3.4.2 Representation of system’s characteristics in terms of transfer function or frequency response ( )( ) ( )( ) 1 0 1 1 1 0 1 1 X s b s b s b s b Y s a s a s a s a m m m m n n n n = + + + + + + + + − − − −   ( ) ( ) ( ) 1 0 1 1 1 0 1 1 a s a s a s a b s b s b s b X s Y s H s n n n n m m m m + + + + + + + + = = − − − −   (3.12)