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I am studying Fourier Transform and it's inverse. We get phase and magnitude from Fourier transform and reconstruct it back from both together

My question is that

  1. What will happen if we try to reconstruct given signal back using it's magnitude only with any random phase values?

  2. What will happen if we try to reconstruct given signal back using it's phase only with any random magnitude values?

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Not in general.

A set of conditions is given in this paper: Hayes, Monson H., Jae S. Lim, and Alan V. Oppenheim. "Signal reconstruction from phase or magnitude." Acoustics, Speech and Signal Processing, IEEE Transactions on 28.6 (1980): 672-680.

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