Essence of transfer functions
For an SISO linear system, it’s transfer function is such that
What essentially does the transfer function mean? It represents nothing but the ratio and phase offset between output and input under different frequencies. By substituting with to the transfer function , we can get the ratio and phase offset. It should be noted that transfer function only describe the relationship between input and output; it is only applicable to linear systems. The analysis of properties of linear systems based on transfer functions form the classic frequency analysis.