3.4.2 Representation of system 's characteristics in terms of transfer function or frequency response 日 Properties: 1) The transfer function H(Wont change with input x(t). It represents only the systems characteristics 2) The system described in terms of its transfer function will provide clearly an output y(t) for any concrete input x( 3)All the coefficients in the equation, an,.aI 0, and 6 m.'01,00, are the constants determined uniquely by the configuration of system
❑ Properties: 1) The transfer function H(s) won ’t change with input x(t). It represents only the system’ s characteristics. 2) The system described in terms of its transfer function will provide clearly an output y(t) for any concrete input x(t). 3) All the coefficients in the equation, an , …a1 , a0 , and bm, …, b1 , b0 , are the constants determined uniquely by the configuration of system. 3.4.2 Representation of system’s characteristics in terms of transfer function or frequency response
3.4.2 Representation of system 's characteristics in terms of transfer function or frequency response 2. Frequency response function For a steady-state LTi system, let s -jo that is, substitute a=0 and b-o in s-=a+jb then Eq(3. 11)changes to Y(o)= y(t)e (3.16) Eq ( 3.16 is an equivalent of the one-sided Fourier transform expression discussed in Chapter 2
2. Frequency response function For a steady-state LTI system, let s=jω, that is, substitute a=0 and b=ω in s=a+jb, then Eq. (3.11) changes to Eq. (3.16) is an equivalent of the one-sided Fourier transform expression discussed in Chapter 2. 3.4.2 Representation of system’s characteristics in terms of transfer function or frequency response − = 0 Y ( j ) y(t)e dt jt (3.16)
3.4.2 Representation of system 's characteristics in terms of transfer function or frequency response In the same manner we have bm gjom+bm- (o)m-l++b, @)+b H(o) (j0)+an1(o)n+…+a1(j0) (3.17) Y(o) X() HGj@) is called the frequency response or frequency response function of a measuring system
In the same manner, we have H(jω) is called the frequency response or frequency response function of a measuring 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 j Y j a j a j a j a b j b j b j b H j n n n n m m m m = + + + + + + + + = − − − − (3.17)
3.4.2 Representation of system 's characteristics in terms of transfer function or frequency response UThe frequency response function is a special case of the transfer function Although both the transfer function and the frequency response can be used to represent the dynamic characteristics of systems, their significances are different
❑The frequency response function is a special case of the transfer function. ❑Although both the transfer function and the frequency response can be used to represent the dynamic characteristics of systems, their significances are different. 3.4.2 Representation of system’s characteristics in terms of transfer function or frequency response