Recovery of phase from first order spectrum

Recovery of phase from magnitude or imaginary part from real part can be accomplished if a signal is well represented by a zero-padded double length data sequence. The zero-padded portion of such double length data can be thought of as a result of cancellation between two double length odd and even signals. Symmetry and anti-symmetry associated with the DFT of even data and odd data warrants the recovery of the phase. A method of deconvolution to reconstruct the original spectrum from zero padded double length data is also presented. This method of phase recovery is applied to an exponentially decaying wave consisting of several spectral components to demonstrate the validity of the method.