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This paper refers to the application of higher-order statistical signal processing techniques cumulant calculation on Gaussian noise cancellation. The performed procedure, joined to a convolution process and Fast Fourier Transform FFT application, results in the complete estimation i.e., amplitude, frequency and phase recovery of any corrupted periodic signal. Whereas tone frequency estimation is performed by 4th-order cumulant calculation, phase recovery is achieved by the convolution of the cumulant calculation and the corrupted signal. At last, the original signal amplitude is recovered by means of modification of the resulting amplitude spectrum. In this paper, higher-order statistics foundations are presented and the validation of the proposed algorithm is revealed in both theoretical and practical sense. Obtained results are highly satisfactory.

Detection of Periodic Signals in Noise Based on Higher-Order Statistics Joined to Convolution Process and Spectral Analysis