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Speech(or Phase) Reconstruction from Magnitude Spectrum

Dear List Members,
I am working on a project where I need to reconstruct a speech signal using only its magnitude spectrum and some relevant phase information. Actually, my signal is bandlimited to 0-4Khz and I even have the phase information of the same signal after it is passed through a bandpass filter of 200-3600Hz. However, when I superimpose this phase information on my signal the resulting speech has some noise which I cannot eliminate using any kind of adapting filter.
Hence my question is...Is it possible to reconstruct speech using only magnitude spectrum? Any comments will be greatly appreciated.
Thank you very much and have a wonderful day !
Ismail Uysal
University of Florida,
CNEL, Ph.D Student

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