Effects of noise on signal reconstruction from Fourier transform phase

The effects of noise in the given phase on signal reconstruction from the Fourier transform phase are studied. Specifically, the effects of different methods of sampling the degraded phase, of the number of non-zero points in the sequence, and of the noise level on the sequence reconstruction are examined. A sampling method is developed to significantly reduce the error in the reconstructed sequence, and the error is found to increase as the number of non-zero points in the sequence increases and as the noise level increases. In addition, an averaging technique is developed which reduces the effects of noise when the continuous phase function is known. Finally, as an illustration of how the results in this paper may be applied in practice, Fourier transform signal coding is considered. Coding only the Fourier transform phase and reconstructing the signal from the coded phase is found to be considerably less efficient (i.e. a higher bit rate is required for the same mean square error) than reconstructing from both the coded phase and magnitude.