Sunday, 5 April 2015

Given Gain function, how to design a causal, stable and minimum phase IIR filter?


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)=1πα(Ω)ωΩdΩ


So ϕ(ω) is uniquely determined by α(ω). This is the corresponding wikipedia entry.


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