Coherence bandwidth of S21
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How do I code this formula in Matlab to find the coherence bandwidth of an S21 data set (a vector of complex numbers vs. frequency)?
Coherence bandwidth is defined according to the correlation function of the frequency response (R(χ)).
R(χ) = ∫ H (f )H∗ (f + χ)df
integrated from fmin to fmax, where χ is the frequency shift, B = [fmin ,fmax ] is the frequency bandwidth and {.}∗ denotes the complex conjugate.
Then, the coherence bandwidth of the channel at the level ρ ∈ [0,1], is defined as the frequency Bρ for which the absolute value of the correlation function falls to a value equal to ρ times its maximum corresponding to χ = 0.
Bρ = χ such that |R(χ)| = ρ|R(0)|
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