JOURNAL OF COMPUTERS (JCP)

ISSN : 1796-203X

Volume : 2 Issue : 7 Date : September 2007

**Algorithms and Applications for Estimating the Standard Deviation of AWGN when Observations **

are not Signal-Free

Dominique Pastor and Asmaa Amehraye

Page(s): 1-10

Full Text: PDF (413 KB)

**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.

ISSN : 1796-203X

Volume : 2 Issue : 7 Date : September 2007

are not Signal-Free

Page(s): 1-10

Full Text: PDF (413 KB)

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.

speech denoising.