¹GET - ENST Bretagne, CNRS TAMCIC (UMR 2872), Technopˆole de Brest Iroise, CS 83818, 29238 BREST Cedex, FRANCE

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Abstract—Consider observations where random signals are randomly present or absent in independent and additive white Gaussian noise (AWGN). By using a recently established limit theorem, we introduce a new estimator for the estimation of the noise standard deviation when the signals are less present than absent and have unknown probability distributions. The bias, the consistency and the minimum attainable mean square estimation error of the estimator we propose are still unknown. However, the experimental results that are presented are very promising. First, when the Minimum- Probability-of-Error decision scheme for the non-coherent detection of modulated sinusoidal carriers in independent AWGN is tuned with the outcome of our estimator instead of the true value of the noise standard deviation, the Binary Error Rate tends to the optimal error probability when the number of observations is large enough. Second, given some speech signal corrupted by independent AWGN, our estimator can be used to estimate the noise standard deviation so as to adjust the standard Wiener filtering of the noisy speech. The objective performance measurements obtained by so proceeding are very close to those achieved when the Wiener filtering is tuned with the true value of the noise standard deviation.

Index Terms—Binary hypothesis testing, decision, estimation, likelihood theory, multivariate normal distribution, speech denoising

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Cite: Dominique Pastor, Asmaa Amehraye, "Algorithms and Applications for Estimating the Standard Deviation of AWGN when Observations are not Signal-Free," Journal of Computers vol. 2, no. 7, pp. 1-10, 2007.