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A technique based on bispectrum averaging is described for generally recovering the signal waveform from a set of noisy signals with variable signal delay. The technique does not require explicit time alignment of signals and any initial estimate of signal. The technique, however, does not yield estimates of the signal position. A comparison is made of two algorithms for recovering the Fourier amplitude and the Fourier phase from an averaged bispectrum. These algorithms are the recursive method and the least squares method. The methods are numerically investigated using computer-generated data and a physiological signal and noise. The advantages and disadvantages of these different algorithms are discussed. Some experimental results for the evoked potential studies that demonstrate the technique are given. The results show the effectiveness of the technique: various potential applications of the technique might be expected.