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if i have the transfer function of magnitude response is there a method that i could calculate the frequency response?

For example the transfer function of the magnitude response is:

$ 3db \pm 3.5db $ for $|ν|<0.1$

$ <-55db $ for $|ν|<0.2$

xkrpz
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2 Answers2

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Without other assumptions, no.

Let $\hat{f_T}(s) = e^{-sT}$, this is the transfer function of a pure delay of $T$, but $|\hat{f_T}(i \omega)| = 1$ for all $\omega$. Hence it is impossible to recover the $T$.

copper.hat
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  • If i understand well we need the frequency. If this filter is a lowpass and operates at a sample rate of 10 Msps? This is the frequency if i dont make a mistake? – xkrpz Feb 25 '13 at 18:28
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In addition to copper.hat's answer, if and only if the system is minimum phase, the natural logarithm of the magnitude response and phase response are related by the Hilbert transform.

P.S. For a causal, stable, linear shift-invariant system, the real and imaginary parts of the transfer function are Hilbert transform pairs, which becomes the Kramers-Kronig relations if the transfer function is real-valued.

chaohuang
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