We give a sufficient condition that insures that the impulse response of a channel is of minimum phase. The condition is that the energy of the first path be larger than the power spectral density of all subsequent paths. Establishing a lower bound to the first path energy, this condition is more likely to be met if transmitter and receiver are in line-of-sight. Our results show that the Hilbert transform may give unreliable results, if used to extract the channel phase response from frequency-resolved amplitude measurements when the first path is strongly attenuated.
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