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.

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. .

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.

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.

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.

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.

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.

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.

Effect of inertial mass on a linear system driven by dichotomous noise and a periodic signal

A linear system driven by dichotomous noise and a periodic signal is investigated in the underdamped case. The exact expressions of output signal amplitude and signal-to-noise ratio （SNR） of the system are derived. By means of numerical calculation, the results indicate that （i） at some fixed noise intensities, the output signal amplitude with inertial mass exhibits the structure of a single peak and single valley, or even two peaks if the dichotomous noise is asymmetric; （ii） in the case of asymmetric dichotomous noise, the inertial mass can cause non-monotonic behaviour of the output signal amplitude with respect to noise intensity; （iii） the curve of SNR versus inertial mass displays a maximum in the case of asymmetric dichotomous noise, i.e., a resonance-like phenomenon, while it decreases monotonically in the case of symmetric dichotomous noise; （iv） if the noise is symmetric, the inertial mass can induce stochastic resonance in 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.

A Novel Peak-to-Average Power Ratio Reduction Scheme via Tone Reservation in OFDM Systems

In this paper, a novel signal-to-clipping noise ratio and least squares approximation tone reservation scheme(SCR-LSA TR) is proposed to reduce the peak-to-average power ratio for orthogonal frequency division multiplexing systems. During the SCR procedure, only the element with the maximal amplitude is picked for processing, which not only decreases the algorithm complexity, but also helps to overcome the BER deterioration. With the LSA method, the amplitude of the peak-cancelling signals can approximate to that of the original clipping noise as much as possible. Through the combination of the optimization factor in the LSA method, the classic SCR method can achieve better PAPR reduction with faster convergence. Simulation results show that the proposed SCR-LSA TR scheme has less in-band distortion and smaller out-of-band spectral radiation. The BER of the proposed scheme shows a better performance especially under the 16-QAM over the additive white Gaussian noise channel.

Combining Radon-ambiguity transform with second-order difference to improve detection probability of LFM signals in low SNR

The Radon-ambiguity transform （RAT）, although efficient for detecting the linear frequency modulated signals （LFMs）, is troubled by the energy accumulation of noise in low signal-to-noise ratio （SNR）. A secondorder difference （SOD） method is proposed to treat with this problem. In the SOD method, the optimal search step and difference step are derived from the LFM rate resolution formula. The sharpness of the peaks of RAT is measured by curvature, and the sharpness, but not the magnitude of the peaks, is used to detect the LFMs. The SOD method removes the noise energy accumulation and reserves the drastically changing components integrally; thus, it improves the detection probability of LFMs in low SNR. The expected performance of the new method is verified by 100 Monte Carlo simulations.

Photoelectric detection technology of laser seeker signals

The measurement of the rolling angle of the projectile is one of the key technologies for the terminal correction projectile.To improve the resolution accuracy of the rolling angle in the laser seeker weapon system, the imaging model of the detector, calculation model of the position and the signal-to-noise ratio(SNR) model of the circuit are built to derive both the correlation between the resolution error of the rolling angle and the spot position, and the relation between the position resolution error and the SNR. Then the influence of each parameter on the SNR is analyzed at large,and the parameters of the circuit are determined. Meanwhile, the SNR and noise voltage of the circuit are calculated according to the SNR model and the decay model of the laser energy. Finally,the actual photoelectric detection circuit is built, whose SNR is measured to be up to 53 d B. It can fully meet the requirement of0.5° for the resolution error of the rolling angle, thereby realizing the analysis of critical technology for photoelectric detection of laser seeker signals.

Implication of two-coupled tri-stable stochastic resonance in weak signal detection

Stochastic resonance （SR） has been proved to be an effective approach to extract weak signals overwhelmed in noise. However, the detection effect of current SR models is still unsatisfactory. Here, a coupled tri-stable stochastic resonance （CTSSR） model is proposed to further increase the output signal-to-noise ratio （SNR） and improve the detection effect of SR. The effects of parameters a, b, c, and r in the proposed resonance system on the SNR are studied, by which we determine a set of parameters that is relatively optimal to implement a comparison with other classical SR models. Numerical experiment results indicate that this proposed model performs better in weak signal detection applications than the classical ones with merits of higher output SNR and better anti-noise capability.

Noise analysis of grating-based x-ray differential phase-contrast imaging with angular signal radiography

X-ray phase-contrast imaging is one of the novel techniques,and has potential to enhance image quality and provide the details of inner structures nondestructively.In this work,we investigate quantitatively signal-to-noise ratio（SNR） of grating-based x-ray phase contrast imaging（GBPCI） system by employing angular signal radiography（ASR）.Moreover,photon statistics and mechanical error that is a major source of noise are investigated in detail.Results show the dependence of SNR on the system parameters and the effects on the extracted absorption,refraction and scattering images.Our conclusions can be used to optimize the system design for upcoming practical applications in the areas such as material science and biomedical imaging.

Investigation on Noise Control Technology of Ultra-High Expansion Ratio Turbine

Aerodynamic noise control is one of the key technologies in the development of stealth technology of torpedo. The noise producing mechanism in an ultra-high expansion ratio turbine with partial admission were discussed. Wide wakes originating from non-outlet region between elliptical nozzles,circumferential non-uniformity owing to partial admission design and complex shock system formed in narrow space between nozzles and rotors are three main sources of aerodynamic noise in this turbine. Thus,two kinds of aerodynamic noise control methods were put forward,namely adding axial gap between the nozzle and rotor,nozzle-down,bilateral repair and trailing edge blowing. Steady annulus simulation results showed that the aerodynamic noise was significantly reduced by more than 10 dB after optimization,which had little impact on the aerodynamic performance of the turbine.

Effect of inertia mass on the stochastic resonance driven by a multiplicative dichotomous noise

A stochastic system driven by dichotomous noise and periodic signal is investigated in the under-damped case.The exact expressions of output signal amplitude and signal-to-noise ratio（SNR） of the system are derived.Numerical results indicate that the inertial mass greatly affects the output signal amplitude and the SNR.Regardless of whether the noise is symmetric or asymmetric,the inertial mass can influence the phenomenon of stochastic resonance（SR） of the system,leading to two types of resonance phenomenon：one is coherence-resonance-like of the SNR with inertial mass,the other is the SR of the SNR with noise intensity.