Using Pearson’s System of Curves to Approximate the Distributions of the Difference between Two Correlated Estimates of Signal-to-Noise Ratios: The Cases of Bivariate Normal and Bivariate Lognormal Distributions

Background: The signal-to-noise ratio (SNR) is recognized as an index of measurements reproducibility. We derive the maximum likelihood estimators of SNR and discuss confidence interval construction on the difference between two correlated SNRs when the readings are from bivariate normal and bivariate lognormal distribution. We use the Pearsons system of curves to approximate the difference between the two estimates and use the bootstrap methods to validate the approximate distributions of the statistic of interest. Methods: The paper uses the delta method to find the first four central moments, and hence the skewness and kurtosis which are important in the determination of the parameters of the Pearsons distribution. Results: The approach is illustrated in two examples;one from veterinary microbiology and food safety data and the other on data from clinical medicine. We derived the four central moments of the target statistics, together with the bootstrap method to evaluate the parameters of Pearsons distribution. The fitted Pearsons curves of Types I and II were recommended based on the available data. The R-codes are also provided to be readily used by the readers.

Adaptive Bistable Stochastic Resonance Based Weak Signal Reception in Additive Laplacian Noise

Weak signal reception is a very important and challenging problem for communication systems especially in the presence of non-Gaussian noise,and in which case the performance of optimal linear correlated receiver degrades dramatically.Aiming at this,a novel uncorrelated reception scheme based on adaptive bistable stochastic resonance(ABSR)for a weak signal in additive Laplacian noise is investigated.By analyzing the key issue that the quantitative cooperative resonance matching relationship between the characteristics of the noisy signal and the nonlinear bistable system,an analytical expression of the bistable system parameters is derived.On this basis,by means of bistable system parameters self-adaptive adjustment,the counterintuitive stochastic resonance(SR)phenomenon can be easily generated at which the random noise is changed into a benefit to assist signal transmission.Finally,it is demonstrated that approximately 8dB bit error ratio(BER)performance improvement for the ABSR-based uncorrelated receiver when compared with the traditional uncorrelated receiver at low signal to noise ratio(SNR)conditions varying from-30dB to-5dB.

Acquisition Practice of High Signal-to-Noise Ratio in YTB Block of Sichuan Basin

YTB block in Sichuan basin is a favorable area to exploit oil and gas in shallow tight rock. 3D seismic project of this zone has two characteristics. Firstly, it has high requirements for the tolerance rate of the construction process and the acquisition of high signal-to-noise ratio seismic data;Second, there are widely obstacles and noises that lead to difficult acquisition construction organization. In acquisition practice, high signal-to-noise ratio seismic data was obtained by reasonable design of construction scheme, optimization of excitation parameters, improvement of receiving conditions and optimization of obstacle crossing observation system. .

An Analytical Theory of the Signal-to-Noise Ratio of Hall Plates with Four Contacts and a Single Mirror Symmetry

This work gives an analytical theory of the signal-to-thermal-noise ratio (SNR) of classical Hall plates with four contacts at small magnetic field. In contrast to previous works, the symmetry of the Hall plates is reduced to only a single mirror axis, whereby the average of potentials of the two output contacts off this mirror axis differs from the average of potentials at the two supply contacts on the mirror axis, i.e. the output common mode differs from 50%. Surprisingly, at fixed power dissipated in the Hall plate, the maximum achievable SNR is only 9% smaller for output common modes of 30% and 70% when compared to the overall optimum at output common modes of 50%. The theory is applied to Vertical Hall effect devices with three contacts on the top surface and one contact being the buried layer in a silicon BiCMOS process. Geometries are found with large contacts and only a moderate loss in SNR.

Noises and Signal-to-Noise Ratio of Nanosize EIS and ISFET Biosensors

The results of comparative theoretical analyzes of the behavior of internal low-frequency noises, signal-to-noise ratio and sensitivity to DNA molecules for EIS and ISFET based nanosize biosensors are presented. It is shown that EIS biosensor is more sensitive to the presence of DNA molecules in aqueous solution than ISFET sensor. Internal electrical noises level decreases with the increase of concentration of DNA molecules in aqueous solution. In the frequency range 10−3 - 103 Hz noises level for EIS sensor about in three orders is higher than for ISFET sensor. In the other hand, signal-to-noise ratio for capacitive EIS biosensor is much higher than for ISFET sensor.

Signal-to-noise ratio of lensless ghost interference with thermal incoherent light

Factors influencing the signal-to-noise ratio （SNR） of lensless ghost interference with thermal incoherent light are investigated. Our result shows that the SNR of lensless ghost interference is related to the transverse length of the object, the position of the object in the imaging system and the transverse size of the light source. Furthermore, the effects of these factors on the SNR are discussed in detail by numerical simulations.

基于轻量化RF算法的高阶QAM信号OSNR估计方法

针对光信噪比(OSNR)估计复杂度高、计算量大的问题,提出了一种基于轻量化随机森林(RF)算法的高阶正交幅度调制(QAM)信号OSNR估计方法。该方法通过将不同OSNR的高阶QAM信号映射为不同的星座图数据集,并利用这些数据集来训练RF模型,从而实现OSNR的快速估计。仿真结果表明:采用基于轻量化RF算法估计64QAM和128QAM信号的OSNR,在系统OSNR真实值为5~30 d B时,2种调制格式的OSNR估计准确率均接近100%;64QAM信号OSNR估计值的平均绝对误差(MAE)为0.08 d B,128QAM的MAE为0.12 d B,比基于长短期记忆(LSTM)算法的信号OSNR估计结果更准确。

Signal-to-noise ratio comparison of angular signal radiography and phase stepping method

Grating-based x-ray phase contrast imaging has the potential to be applied in future medical applications as it is compatible with both laboratory and synchrotron source. However, information retrieval methods are important because acquisition speed, scanning mode, image quality, and radiation dose depend on them. Phase-stepping （PS） is a widely used method to retrieve information, while angular signal radiography （ASR） is a newly established method. In this manuscript, signal-to-noise ratios （SNRs） of ASR are compared with that of PS. Numerical experiments are performed to validate theoretical results. SNRs comparison shows that for refraction and scattering images ASR has higher SNR than PS method, while for absorption image both methods have same SNR. Therefore, our conclusions would have guideline in future preclinical and clinical applications.

A blind source separation algorithm based on negentropy and signal noise ratio

A novel blind source separation （BSS） algorithm based on the combination of negentropy and signal noise ratio （SNR） is presented to solve the deficiency of the traditional independent component analysis （ICA） algorithm after the introduction of the principle and algorithm of ICA. The main formulas in the novel algorithm are elaborated and the idiographic steps of the algorithm are given. Then the computer simulation is used to test the performance of this algorithm. Both the traditional FastlCA algorithm and the novel ICA algorithm are applied to separate mixed signal data. Experiment results show the novel method has a better performance in separating signals than the traditional FastlCA algorithm based on negentropy. The novel algorithm could estimate the source signals from the mixed signals more precisely.

Enhancement of signal-to-noise ratio of ultracold polar NaCs molecular spectra by phase locking detection

We report a method of high-sensitively detecting the weak signal in photoassociation （PA） spectra of ultracold NaCs molecules by phase sensitive-demodulated trap-loss spectra of Na atoms from a photomultiplier tube. We find that the signal-to-noise ratio （SNR） of the PA spectra is strongly dependent on the integration time and the sensitivity of the lock-in amplifier, and our results show reasonable agreement with the theoretical analyses of the SNR with the demodulation parameters. Meanwhile, we investigate the effect of the interaction time of the PA laser with the colliding Na-Cs atom pairs on the SNR of the PA spectra. The atom loss rate is dependent on both the PA-induced atom loss and the loading of the MOT. The high-sensitive detection of the excited ultracold NaCs molecules lays a solid foundation for further study of the formation and application of ultracold NaCs molecules.

Local Correlated Noise Improvement of Signal-to-Noise Ratio Gain in an Ensemble of Noisy Neuron

We theoretically investigate the collective response of an ensemble of leaky integrate-and-fire neuron units to a noisy periodic signal by including local spatially correlated noise. By using the linear response theory, we obtained the analytic expression of signal-to-noise ratio (SNR). Numerical simulation results show that the rms amplitude of internal noise can be increased up to?an optimal value where the output SNR reaches a maximum value. Due to the existence of the local spatially correlated noise in the units of the ensemble, the SNR gain of the collective ensemble response can exceed unity and can be optimized when the nearest-neighborhood correlation is negative. This nonlinear collective phenomenon of SNR gain amplification in an ensemble of leaky integrate-and-fire neuron units can be related to the array stochastic resonance (SR) phenomenon. Furthermore, we also show that the SNR gain can also be optimized by tuning the number of neuron units, frequency and?amplitude of the weak periodic signal. The present study illustrates the potential to utilize the local spatially correlation noise and the number of ensemble units for optimizing the collective response of the neuron to inputs, as well as a guidance in the design of information processing devices to weak signal detection.

Study of signal-to-noise ratio driven by colored noise

This paper investigates the signal-to-noise ratio(SNR)driven by colored noise and weak input signals.Based on the Cauchy-Schwarz and Rayleigh quotients inequalities,an analytical expression of SNR is developed,and its upper band is closely related to the Fisher information of noise.For mimicking the colored noise,we adopt the first-order moving-average model and propose the optimal input signal waveform.The stochastic resonance effect in threshold systems is demonstrated for the Gaussian mixture colored noise.The obtained results will be interesting in the case of improving the nonlinear filter performance by adding noise to the weak signal corrupted by the colored noise.

基于SNRgram方法的滚动轴承故障特征提取

针对平方包络信号的负熵对随机脉冲敏感以及平方包络谱的负熵易受离散谐波干扰,从而导致信息图法对随机脉冲和离散谐波分析时鲁棒性差的问题,引入信噪比测度作为轴承故障信息的评估指标,识别包含丰富故障信息的共振频带,并进一步提出基于SNRgram的包络分析方法提取滚动轴承故障特征。仿真和试验结果表明,相对于信息图和其他典型频带识别方法,SNRgram方法处理随机脉冲和离散谐波时具有更强的鲁棒性以及更高的频带识别准确性,能够有效识别轴承故障相关共振频带并提取轴承故障脉冲特征。

Analysis of EMD Algorithm for Identification and Extraction of An Acoustic Signal in Underwater Channel Against Wind Driven Ambient Noise

Sonar generated acoustic signals transmitted in underwater channel for distant communications are affected by numerous factors like ambient noise, making them nonlinear and non-stationary in nature. In recent years, the application of Empirical Mode Decomposition(EMD) technique to analyze nonlinear and non-stationary signals has gained much attention. It is an empirical approach to decompose a signal into a set of oscillatory modes known as intrinsic mode functions(IMFs). In general, Hilbert transform is used in EMD for the identification of oscillatory signals. In this paper a new EMD algorithm is proposed using FFT to identify and extract the acoustic signals available in the underwater channel that are corrupted due to various ambient noises over a range of 100 Hz to 10 kHz in a shallow water region. Data for analysis are collected at a depth of 5 m and 10 m offshore Chennai at the Bay of Bengal. The algorithm is validated for different sets of known and unknown reference signals. It is observed that the proposed EMD algorithm identifies and extracts the reference signals against various ambient noises. Significant SNR improvement is also achieved for underwater acoustic signals.

A NOVEL METHOD FOR ESTIMATING THE SNR OF UNKNOWN EMITTER SIGNAL

It is important to estimate the Signal-to-Noise Ratio(SNR) of unknown emitter signal accurately.In order to resolve the disadvantages of present algorithm,a novel method is proposed in this letter.We extract and normalize the information of zero frequency of received signal by the Wigner-Vile Distribution(WVD) transformation and then get the approximate power of original signal by mathematic transformation,at last,we get the estimate value of SNR by the known account formula of SNR.Simulation results show that it is correct and feasible.

A BLIND SNR ESTIMATOR FOR DIGITAL BANDPASS SIGNALS

A subspace-based blind Signal-to-Noise Ratio (SNR) estimation algorithm for digital bandpass signals in Additive White Gaussian Noise (AWGN) channel is discussed. The lower bounds of the mean and variance of the estimation are derived, and simulations are performed for the commonly used digital bandpass signals, such as MPSK (M=2, 4, 8), MFSK (M=2, 4) and MQAM (M=16, 64, 128, 256) signals. Theoretical analyses and simulation results indicate that the proposed algorithm is ef- fective even when the SNR is below 0dB. Furthermore, the algorithm can provide a blind estimator in that it needs neither the parameters of the received signals, such as the carrier frequency, symbol rate and modulation scheme, nor the synchronization of the system.

An improved joint method for onset picking of acoustic emission signals with noise

The onset times of acoustic signals with spikes,heavy bodies and unclear takeoffs are difficult to be picked accurately by the automatic method at present.To deal with this problem,an improved joint method based on the discrete wavelet transform(DWT),modified energy ratio(MER)and Akaike information criterion(AIC)pickers,has been proposed in this study.First,the DWT is used to decompose the signal into various components.Then,the joint application of MER and AIC pickers is carried out to pick the initial onset times of all selected components,where the minimum AIC position ahead of MER onset time is regarded as the initial onset time.Last,the average for initial onset times of all selected components is calculated as the final onset time of this signal.This improved joint method is tested and validated by the acoustic signals with different signal to noise ratios(SNRs)and waveforms.The results show that the improved joint method is not affected by the variations of SNR,and the onset times picked by this method are always accurate in different SNRs.Moreover,the onset times of all acoustic signals with spikes,heavy bodies and unclear takeoffs can be accurately picked by the improved joint method.Compared to some other methods including MER,AIC,DWT-MER and DWT-AIC,the improved joint method has better SNR stabilities and waveform adaptabilities.

Underwater acoustic signal extraction algorithm in a strong noise environment

In the exploration,tracking and positioning of underwater targets,it is necessary to perform frequency domain analysis and correlation calculation on the underwater acoustic signals of the target radiation.In a strong noise environment,the target signal may be overwhelmed by noise,resulting in an inability to effectively identify the target.Aiming at this problem,this paper presents a method of signal-noise separation by combining Fourier denoising with wavelet transform to realize underwater acoustic signal extraction in a strong noise environment.The combination algorithm of Fourier coefficient threshold adjustment and wavelet threshold transform is designed,and performance of the algorithm is tested.Simulation results show that the combination algorithm can effectively extract underwater acoustic signals when signal-to-noise ratio(SNR)is-15 dB,which can improve the SNR to 8.2 dB.

飞行时间、点扩散函数和高斯滤波对18F-FDG PET/CT肺结节SUV和SNR的影响

目的:探讨飞行时间(TOF)、点扩展函数(PSF)和高斯滤波(GF)对肺结节的标准化摄取值(SUV)和信噪比(SNR)的影响,为肺结节患者提供最佳的PET重建算法.方法:回顾性分析2020年12月至2022年3月在安徽医科大学第一附属医院行全身18F-FDGPET/CT检查的38例肺结节患者的PET/CT图像.采用滤波反投影(FBP)、有序子集最大期望值(OSEM)、OSEM+TOF、OSEM+PSF、OSEM+TOF+PSF和OSEM+TOF+PSF+GF[GF的半高宽(FWHM)分别为2、4、6、8和10 mm]重建算法进行图像重建,通过视觉评估PET图像质量和半定量方法分析肺结节的SNR和SUV.分别采用Holm-Sidak检验和Friedman检验分析不同重建算法间SUV和SNR的差异.结果:相比于FBP组,OSEM+TOF+PSF组SUVmax、SUVpeak、SUVmean 和 SNR 分别提高 8.02%(P>0.05)、10.72%(P<0.000 1)、19.05%(P<0.000 1)和 688.89%(P<0.000 1);相比于OSEM组,OSEM+TOF+PSF组SUVmax、SUVpeak、SUVmean和SNR分别提高 13.89%、25.60%、38.56%和 101.07%(均P<0.01);相比于OSEM+TOF组,OSEM+TOF+PSF组SUVpeak、SUVmean和SNR分别提高8.42%、12.76%和67.98%(均P<0.000 1),SUVmax降低2.76%(P>0.05);相比于OSEM+PSF组,OSEM+TOF+PSF组 SUVmax、SUVpeak、SUVmean 和 SNR分别提高 28.17%、19.19%、33.83%和12.15%(均 P<0.01).与 OSEM+TOF+PSF 组相比,OSEM+TOF+PSF+GF(2 mm FWHM)组 SUVmax、SUVpeak和SUVmean分别降低 12.12%、52.05%和9.24%,SNR提高3.42%(均P<0.05);OSEM+TOF+PSF+GF(4 mm FWHM)组 SUVmax、SUVpeak 和 SUVmean 分别降低 56.67%、69.79%和 34.75%,SNR 提高10.10%(均P<0.05);OSEM+TOF+PSF+GF(6 mm FWHM)组SUVmax、SUVpeak、SUVmean和SNR分别降低 115.91%、99.10%、73.63%和 1.75%(均P<0.05);OSEM+TOF+PSF+GF(8 mm FWHM)组 SUVmax、SUVpeak、SUVmean 和 SNR 分别降低 198.38%、140.65%、126.04%和 18.68%(均P<0.05);OSEM+TOF+PSF+GF(10 mm FWHM)组 SUVmax、SUVpeak、SUVmean和 SNR分别降低 311.94%、198.99%、201.85%和60.47%(均P<0.05).2名医师对FBP、OSEM、OSEM+TOF、OSEM+PSF和OSEM+TOF+PSF重建算法肺结节PET图像视觉评分优秀率均值分别为0、11.63%、25.58%、18.60%和50.00%;OSEM+TOF+PSF+GF(GF的FWHM分别为2、4、6、8和10mm)重建算法肺结节PET图像视觉评分优秀率均值分别为51.16%、54.65%、54.65%、33.72%和 10.47%.结论:在所有重建算法中,OSEM+TOF+PSF+GF(4 mm FWHM)重建算法可以获得最佳的肺结节PET图像视觉评分和SNR,但降低了肺结节的SUV.

Long term integration of radar signals with unknown Doppler shift for ubiquitous radar

Ubiquitous radar is a new radar system that provides continuous and uninterrupted multifunction capability within a coverage volume. Continuous coverage from close-in ＂pop-up＂ targets in clutter to long-range targets impacts selection of waveform parameters. The coherent processing interval （CPI） must be long enough to achieve a certain signal-to-noise ratio （SNR） that ensures the efficiency of detection. The condition of detection in the case of low SNR is analyzed, and three different cases that would occur during integration are discussed and a method to determine the CPI is presented. The simulation results show that targets detection with SNR as low as -26 dB in the experimental system can possibly determine the CPI.