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Essence of transfer functions

17/04/2011

For an SISO linear system, it’s transfer function is T(s) such that

y=T(s)u

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 s with j\omega to the transfer function T(s), 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.

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