White Gaussian Noise – Models for Engineers

Frequenz ◽  
2018 ◽  
Vol 72 (5-6) ◽  
pp. 293-299
Author(s):  
Friedrich K. Jondral
Keyword(s):  
Mathematical Models ◽  
Gaussian Noise ◽  
Signal To Noise Ratio ◽  
White Gaussian Noise ◽  
Second Step ◽  
Measurement Technology ◽  
Practical Application ◽  
Irregular Motion ◽  
Important Quality ◽  
Noise Models

AbstractThis paper assembles some information about white Gaussian noise (WGN) and its applications. It starts from a description of thermal noise, i. e. the irregular motion of free charge carriers in electronic devices. In a second step, mathematical models of WGN processes and their most important parameters, especially autocorrelation functions and power spectrum densities, are introduced. In order to proceed from mathematical models to simulations, we discuss the generation of normally distributed random numbers. The signal-to-noise ratio as the most important quality measure used in communications, control or measurement technology is accurately introduced. As a practical application of WGN, the transmission of quadrature amplitude modulated (QAM) signals over additive WGN channels together with the optimum maximum likelihood (ML) detector is considered in a demonstrative and intuitive way.

scholarly journals Smooth Signal Activity Detection in White Gaussian Noise: Application to P300 Detection

2021 ◽  
Author(s):  
Ali Mobaien ◽  
Reza Boostani ◽  
Negar Kheirandish
Keyword(s):  
Gaussian Noise ◽  
Signal To Noise Ratio ◽  
Hypothesis Test ◽  
White Gaussian Noise ◽  
Least Square ◽  
Unknown Parameters ◽  
Detection Scheme ◽  
Ml Estimation ◽  
Unknown Variance ◽  
Synthetic Datasets

<div>Abstract—In this research, we have proposed a new scheme to detect and extract the activity of an unknown smooth template in presence of white Gaussian noise with unknown variance. In this regard, the problem is considered a binary hypothesis test, and it is solved employing the generalized likelihood ratio (GLR) method. GLR test uses the maximum likelihood (ML) estimation of unknown parameters under each hypothesis. The ML estimation of the desired signal yields an optimization problem with smoothness constraint which is in the form of a conventional least square error estimation problem and can be solved optimally. The proposed detection scheme is studied for P300 elicitation from the background electroencephalography signal. In addition, to assume the P300 smoothness, two prior knowledge are considered in terms of positivity and approximate occurrence time of P300. The performance of the method is assessed on both real and synthetic datasets in different noise levels and compared to a conventional signal detection scheme without considering smoothness priors, as well as state-of-theart linear and quadratic discriminant analysis. The results are illustrated in terms of detection probability, false alarm rate, and accuracy. The proposed method outperforms the counterparts in low signal-to-noise ratio situations.</div>

scholarly journals Sensitivity of the General Linear Model to Assumptions

2020 ◽  
Vol 6 (5) ◽  
pp. 21-25
Keyword(s):  
Linear Model ◽  
Gaussian Noise ◽  
Linear Models ◽  
General Linear Model ◽  
White Gaussian Noise ◽  
General Linear ◽  
Optimal Estimator ◽  
Significant Performance ◽  
Non Gaussian ◽  
Noise Models

Non-Gaussian noise often causes in significant performance abatement for systems which are designed using Gaussian assumption. This report challenges the question of General Linear Model with White Gaussian Noise assumption in order to define the sensitivity of the performance of an optimal estimator. Gaussian noise models provide an important role in many signal processing applications. The Laplacian and Uniform signal are two worthy examples of noise that can be compared to the White Gaussian Noise, though the sensitivity which can be compared with any non-Gaussian. White Gaussian Noise has been considered for General Linear Models and deviation from whiteness would affect on our estimates under different circumstances. Moreover, new assumptions have been considered to generate different type of signals in order to evaluate the sensitivity of the General Linear Model.

scholarly journals Encrypted message transmission in a QO-STBC encoded MISO wireless Communication system under implementation of low complexity ML decoding algorithm

2012 ◽  
Vol 2 (2) ◽  
pp. 53-58
Author(s):  
Shaikh Enayet Ullah ◽  
Md. Golam Rashed ◽  
Most. Farjana Sharmin
Keyword(s):  
Fading Channels ◽  
Gaussian Noise ◽  
Communication System ◽  
Channel Coding ◽  
Signal To Noise Ratio ◽  
Additive White Gaussian Noise ◽  
Text Message ◽  
Low Complexity ◽  
White Gaussian Noise ◽  
Message Transmission

In this paper, we made a comprehensive BER simulation study of a quasi- orthogonal space time block encoded (QO-STBC) multiple-input single output(MISO) system. The communication system under investigation has incorporated four digital modulations (QPSK, QAM, 16PSK and 16QAM) over an Additative White Gaussian Noise (AWGN) and Raleigh fading channels for three transmit and one receive antennas. In its FEC channel coding section, three schemes such as Cyclic, Reed-Solomon and ½-rated convolutionally encoding have been used. Under implementation of merely low complexity ML decoding based channel estimation and RSA cryptographic encoding /decoding algorithms, it is observable from conducted simulation test on encrypted text message transmission that the communication system with QAM digital modulation and ½-rated convolutionally encoding techniques is highly effective to combat inherent interferences under Raleigh fading and additive white Gaussian noise (AWGN) channels. It is also noticeable from the study that the retrieving performance of the communication system degrades with the lowering of the signal to noise ratio (SNR) and increasing in order of modulation.

A Bayesian Multiresolution Approach for Noise Removal in Medical Magnetic Resonance Images

2018 ◽  
Vol 29 (1) ◽  
pp. 189-201 ◽  
Author(s):  
Sima Sahu ◽  
Harsh Vikram Singh ◽  
Basant Kumar ◽  
Amit Kumar Singh
Keyword(s):  
Magnetic Resonance ◽  
Bayesian Approach ◽  
Gaussian Noise ◽  
Signal To Noise Ratio ◽  
Noise Removal ◽  
White Gaussian Noise ◽  
Error Estimator ◽  
Wavelet Coefficients ◽  
Signal To Noise ◽  
Noise Ratio

Abstract A Bayesian approach using wavelet coefficient modeling is proposed for de-noising additive white Gaussian noise in medical magnetic resonance imaging (MRI). In a parallel acquisition process, the magnetic resonance image is affected by white Gaussian noise, which is additive in nature. A normal inverse Gaussian probability distribution function is taken for modeling the wavelet coefficients. A Bayesian approach is implemented for filtering the noisy wavelet coefficients. The maximum likelihood estimator and median absolute deviation estimator are used to find the signal parameters, signal variances, and noise variances of the distribution. The minimum mean square error estimator is used for estimating the true wavelet coefficients. The proposed method is simulated on MRI. Performance and image quality parameters show that the proposed method has the capability to reduce the noise more effectively than other state-of-the-art methods. The proposed method provides 8.83%, 2.02%, 6.61%, and 30.74% improvement in peak signal-to-noise ratio, structure similarity index, Pratt’s figure of merit, and Bhattacharyya coefficient, respectively, over existing well-accepted methods. The effectiveness of the proposed method is evaluated by using the mean squared difference (MSD) parameter. MSD shows the degree of dissimilarity and is 0.000324 for the proposed method, which is less than that of the other existing methods and proves the effectiveness of the proposed method. Experimental results show that the proposed method is capable of achieving better signal-to-noise ratio performance than other tested de-noising methods.

scholarly journals Smooth Signal Activity Detection in White Gaussian Noise: Application to P300 Detection

2021 ◽  
Author(s):  
Ali Mobaien ◽  
Reza Boostani ◽  
Negar Kheirandish
Keyword(s):  
Gaussian Noise ◽  
Signal To Noise Ratio ◽  
Hypothesis Test ◽  
White Gaussian Noise ◽  
Least Square ◽  
Unknown Parameters ◽  
Detection Scheme ◽  
Ml Estimation ◽  
Unknown Variance ◽  
Synthetic Datasets

<div>Abstract—In this research, we have proposed a new scheme to detect and extract the activity of an unknown smooth template in presence of white Gaussian noise with unknown variance. In this regard, the problem is considered a binary hypothesis test, and it is solved employing the generalized likelihood ratio (GLR) method. GLR test uses the maximum likelihood (ML) estimation of unknown parameters under each hypothesis. The ML estimation of the desired signal yields an optimization problem with smoothness constraint which is in the form of a conventional least square error estimation problem and can be solved optimally. The proposed detection scheme is studied for P300 elicitation from the background electroencephalography signal. In addition, to assume the P300 smoothness, two prior knowledge are considered in terms of positivity and approximate occurrence time of P300. The performance of the method is assessed on both real and synthetic datasets in different noise levels and compared to a conventional signal detection scheme without considering smoothness priors, as well as state-of-theart linear and quadratic discriminant analysis. The results are illustrated in terms of detection probability, false alarm rate, and accuracy. The proposed method outperforms the counterparts in low signal-to-noise ratio situations.</div>

scholarly journals Effects of white Gaussian noise on dynamic balance in healthy young adults

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ziyou Zhou ◽  
Can Wu ◽  
Zhen Hu ◽  
Yujuan Chai ◽  
Kai Chen ◽  
...  
Keyword(s):  
Young Adults ◽  
Gaussian Noise ◽  
Center Of Pressure ◽  
Dynamic Balance ◽  
White Gaussian Noise ◽  
Fluctuation Analysis ◽  
Balance Performance ◽  
Short Term ◽  
Crossover Point ◽  
Short Time

AbstractIt has been known that short-time auditory stimulation can contribute to the improvement of the balancing ability of the human body. The present study aims to explore the effects of white Gaussian noise (WGN) of different intensities and frequencies on dynamic balance performance in healthy young adults. A total of 20 healthy young participants were asked to stand at a dynamic balance force platform, which swung along the x-axis with an amplitude of ± 4° and frequency of 1 Hz. Their center of pressure (COP) trajectories were recorded when they were stimulated by WGN of different intensities (block 1) and different frequencies (block 2). A traditional method and detrended fluctuation analysis (DFA) were used for data preprocessing. The authors found that only with 75–85 dB WGN, the COP parameters improved. WGN frequency did not affect the dynamic balance performance of all the participants. The DFA results indicated stimulation with 75 dB WGN enhanced the short-term index and reduced the crossover point. Stimulation with 500 Hz and 2500 Hz WGN significantly enhanced the short-term index. These results suggest that 75 dB WGN and 500 Hz and 2500 Hz WGN improved the participants’ dynamic balance performance. The results of this study indicate that a certain intensity of WGN is indispensable to achieve a remarkable improvement in dynamic balance. The DFA results suggest that WGN only affected the short-term persistence, indicating the potential of WGN being considered as an adjuvant therapy in low-speed rehabilitation training.

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