I am given |H(ω)|, I wonder if minimum phase stable causal filter is unique and how to calculate it.
Answer
If H(ω)=eα(ω)+jϕ(ω) is a minimum phase frequency response, then the attenuation α(ω) and the phase ϕ(ω) are related by the following Hilbert transform relationship:
ϕ(ω)=−1π∫∞−∞α(Ω)ω−ΩdΩ
So ϕ(ω) is uniquely determined by α(ω). This is the corresponding wikipedia entry.
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