Effects of additive noise on signal reconstruction from Fourier transform phase

The effects of additive noise in the given phase on signal reconstruction from the Fourier transform phase are experimentally studied. Specifically, the effects on the sequence reconstruction of different methods of sampling the degraded phase of the number of nonzero points in the sequence, and of the noise level, are examined. A sampling method that significantly reduces the error in the reconstructed sequence is obtained, and the error is found to increase as the number of nonzero 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.