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Linked below is a previous post regarding a multipath channel.

Equalisation of FFT spectra

I am reusing the images here:

Unperturbed channel

Perturbed channel

The first image is that of the power spectra when there is no multipath and the second is when there is multipath. The phase information of the signal is missing, only the magnitude response is available. There are three ideas but I donot possess the mathematical background to confirm whether or not the three ideas below are right or wrong.

  1. I speculate dividing the perturbed response to the unperturbed response will hold some information about the channel (a form of deconvolution). This is a valid method but how does one interpret the result of the division?
  2. The iFT of this result of division will provide the real-impulse response of the channel.
  3. As a further step Hilbert transform of the real impulse response will provide the complex impulse response of the channel.

Are ideas 2 and 3 valid?

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