One to one mapping between bode plot and transfer function

Is it possible that Bode plot can have multiple transfer functions in S domain or there is always one to one mapping between perticular bode plot and transfer function... Actually I have to design filter and I have its bode plot. I have derived corresponding transfer function .But it is of order 5 and I want to have transfer function with lower order. So is it possible to have lower order filter with same bode plot response

Answer 1

[Arkadiy Turevskiy]

Leaving aside the theoretical part of the question, you can use command tfest from System Identification Toolbox to identify a transfer function of specified order from frequency domain data.