Gaussian Signals Research Articles

Distribution of the multiple coherence estimate for the detection of periodic signals in noise

The sampling distribution of the multiple coherence estimate between one periodic, deterministic signal and a set of N other Gaussian-distributed ones has been derived. This has been accomplished based on a relationship between the estimate and the Hotelling's T2 statistic extended to complex variables and further on another one involving the noncentral F and beta distributions. The obtained probability density function (PDF) was confirmed by means of simulation, which was also used to evaluate the sampling distribution of another multivariate detector. The PDF reduces to that of the univariate case when N is set to one and the zero-coherence case is easily assessed by setting the noncentrality parameter to zero. This expression also holds for the multiple coherence involving only Gaussian signals. Therefore, the multivariate extension of the well-known invariance of simple coherence estimate with respect to second signal provided the first is Gaussian and coherence is zero is now proved. An illustrating example with simulated signals is also provided. The results in this communication may be useful, for example, in investigations involving the multichannel electroencephalogram during sensory stimulation for monitoring of surgeries or in brain-computer interfaces, where one aims at detecting the evoked responses as fast as possible.

Assessment of the Kernel Gram Matrix Representation of Data in Order to Avoid the Alignment of Chromatographic Signals.

This article discusses the possibility of exploratory data analysis of samples described by second-order chromatographic data affected by peak shifts. In particular, the potential of the kernel Gram matrix representation as an alternative to the necessary and time-consuming alignment step is evaluated. It was demonstrated through several simulation studies and comparisons that even small peak shifts can be a substantial source of data variance, and they can easily hamper the interpretation of chromatographic data. When peak shifts are small, their negative effect is far more destructive than the impact of relatively large levels of the Gaussian noise, heteroscedastic noise, and signal’s baseline. The Gram principal component analysis approach has proven to be a well-suited tool for exploratory analysis of chromatographic signals collected using the diode-array detector in which sample-to-sample peak shifts were observed.

Iterative Receiver Design for the Estimation of Gaussian Samples in Impulsive Noise

Impulsive noise is the main limiting factor for transmission over channels affected by electromagnetic interference. We study the estimation of (correlated) Gaussian signals in an impulsive noise scenario. In this work, we analyze some of the existing, as well as some novel estimation algorithms. Their performance is compared, for the first time, for different channel conditions, including the Markov–Middleton scenario, where the impulsive noise switches between different noise states. Following a modern approach in digital communications, the receiver design is based on a factor graph model and implements a message passing algorithm. The correlation among signal samples, as well as among noise states brings about a loopy factor graph, where an iterative message passing scheme should be employed. As is well known, approximate variational inference techniques are necessary in these cases. We propose and analyze different algorithms and provide a complete performance comparison among them, showing that the expectation propagation, transparent propagation, and parallel iterative schedule approaches reach a performance close to optimal, at different channel conditions.

Aggregative Efficiency of Bayesian Learning in Networks

When individuals in a social network learn about an unknown state from private signals and neighbors' actions, the network structure often causes information loss. We consider rational agents and Gaussian signals in the canonical sequential social-learning problem and ask how the network changes the efficiency of signal aggregation. Rational actions in our model are a log-linear function of observations and admit a signal-counting interpretation of accuracy. This generates a fine-grained ranking of networks based on their aggregative efficiency index. Networks where agents observe multiple neighbors but not their common predecessors confound information, and we show confounding can make learning very inefficient. In a class of networks where agents move in generations and observe the previous generation, aggregative efficiency is a simple function of network parameters: increasing in observations and decreasing in confounding. Generations after the first contribute very little additional information due to confounding, even when generations are arbitrarily large.

Granger Causality of Gaussian Signals from Binary or Non-uniformly Quantized Measurements

This paper studies the assessment of Granger causality between jointly Gaussian signals from binary/non-uniformly quantized measurements. A necessary and sufficient condition is proposed for Granger causality inference under binary quantization. Furthermore, sufficient conditions are introduced to infer Granger causality between jointly Gaussian signals through non-uniformly quantized measurements. No assumptions are made on the identifiability of the jointly Gaussian random processes through the quantized observations.

Signal Processing Methods to Enhance the Energy Efficiency of In-Memory Computing Architectures

This paper presents signal processing methods to enhance the energy vs. accuracy trade-off of in-memory computing (IMC) architectures. First, an optimal clipping criterion (OCC) for signal quantization is proposed in order to minimize the precision of column analog-to-digital converters (ADCs) at iso-accuracy. For a Gaussian distributed signal, the OCC is shown to reduce the column ADC precision requirements by 3 bits at an signal-to-quantization noise ratio (SQNR) of 22.5 dB over the commonly used full range (FR) quantizer. Next, the input-sliced weight-parallel (ISWP) IMC architecture is presented as a generalization of the popular bit-serial bit-parallel (BSBP) architecture. Quantization noise analysis of the ISWP indicates that its accuracy is comparable to BSBP while providing an order-of-magnitude reduction in energy consumption due to fewer array invocations and smaller ADC precision. Combining OCC and ISWP noise analysis, we map popular DNNs such as VGG-9 (CIFAR-10), ResNet-18 (CIFAR-10), and AlexNet (ImageNet) on a OCC-enabled ISWP architecture and show a reduction in energy consumption by an order-of-magnitude at iso-accuracy over the BSBP architecture that employs FR-based ADCs.

Algorithms for automatic detection and recognition of low contrast radar objects using noise-like broadband signals

An algorithm for automatic detection and recognition of low-contrast ground targets using noise-like broadband signals and the use of combined processing of radar signals against the background of interference is presented; the proposed original method for processing signals from airborne objects during their detection and determination of their coordinates synthesizes optimal algorithms for detecting radar objects in the case of a priori information about useful signals and interference, as well as the ability to determine the range and speed of movement; the block diagram of the mathematical model of signal processing is considered on the basis of the developed algorithms for identifying stationary targets against the background of local objects by the radar portrait, as well as by the envelope of the radar signal; the results of testing mathematical modeling of the algorithm for recognizing signals from stationary targets and a forest with an equal probability of the appearance of these targets in the analyzed space are presented. The results of domestic theoretical and experimental research today characterize the main areas of research in the field of detection and recognition of various radar objects. The main research tool of most works is the search and development of promising mathematical models of objects and the modeling of secondary radiation for their recognition, which in some cases allows obtaining additional information about these objects. Correlation and spectral methods of their processing are currently being considered in relation to the noise sounding signal of a radar station. This article analyzes the application of correlation and spectral methods in processing noise signals with the identification of the disadvantages and advantages of each of the methods; the functioning of the block diagram of the known single-channel noise radar stations with sequential spectral processing of the total signal is considered. The proposed original method for processing signals from airborne objects during their detection and determination of their coordinates synthesizes optimal algorithms for detecting targets in the case of a priori information about useful signals and interference, as well as the ability to determine the distance and speed of movement. It should be noted the promising application of combined processing of radar signals against the background of interference, taking into account simultaneously the spatial, polarization, temporal and frequency features of the signals reflected from objects. With regard to the problem of recognizing the shape of objects, both in Russia and abroad, intensive work is being carried out to improve the resolution of on-board radars with a synthesized broadband antenna array, while raising the range resolution and increasing the angular resolution allow obtaining long-range portraits of these objects, as well as seeing them. elements and obtain images of targets. In the study of methods for detecting radar objects based on Gaussian noise signals with a large base, it is shown that such signals are promising for detecting subtle objects at ranges greater than with conventional monopulse radar. When receiving noise signals with a large base, spectral methods of signal extraction turn out to be more advantageous in comparison with the known correlation method of signal processing. Based on the use of noise signals, recognition of ground and air objects is realized, while the method of long-range portraits can have an advantage over the envelope method. Based on the results of mathematical modeling, the possibility of automatic recognition of stationary ground objects by two different methods was confirmed with a high probability of their recognition.

Convolutional Maximum-Likelihood Distortionless Response Beamforming With Steering Vector Estimation for Robust Speech Recognition

Beamforming has been one of the most successful approaches using multi-microphones for robust speech recognition. Although a beamforming method, called the “maximum-likelihood distortionless response (MLDR)” beamformer, was recently presented to achieve promising performance, it requires an accurate steering vector for a target speaker in advance like many kinds of beamformers. In this paper, we present a method for steering vector estimation (SVE) by replacing the noise spatial covariance matrix estimate with a normalized version of the variance-weighted spatial covariance matrix estimate for the observed noisy speech signal obtained by the iterative update rule in the MLDR beamforming framework. In addition, an MLDR beamforming method without a steering vector for a target speaker given in advance is presented where the SVE and the beamforming are alternately repeated. Furthermore, an online algorithm based on recursive least squares (RLS) is derived to cope with various practical applications including time-varying situations, and the power method is introduced for further efficient online processing. We also present batch and online convolutional MLDR beamforming with SVE for simultaneous beamforming and dereverberation where the weighted prediction error (WPE) dereverberation and the MLDR beamforming with the SVE were jointly optimized based on the maximum-likelihood estimation (MLE) for a zero-mean complex Gaussian signal with time-varying variances. Moreover, input signals masked by a neural network (NN) for estimating target speech or noise components can be used to further improve the presented beamformers. Experimental results on the CHiME-4 and REVERB challenge datasets demonstrate the effectiveness of the presented methods.

Uncertainty principles for the short-time linear canonical transform of complex signals

The short-time linear canonical transform (STLCT) is a novel time-frequency analysis tool. In this paper, we generalize some different uncertainty principles for the STLCT of complex signals. Firstly, a new uncertainty principle for STLCT of complex signals in time and frequency domains is explored. Secondly, an uncertainty principle in two STLCT domains is obtained. They show that the lower bounds are related to the covariance of time and frequency and can be achieved by complex chirp signals with Gaussian signals. Then the uncertainty principle for the two conditional standard deviations of the spectrogram associated with the STLCT is derived. In addition, an example is also carried out to verify the correctness of the theoretical analyses. Finally, some potential applications are presented to show the effectiveness of the theorems.

Generation of non-Gaussian stationary random excitations with specified cross-power spectral densities using zero memory non-linear transformation for fatigue test purposes

Zero-memory non-linear (ZMNL) methods have long been a type of very useful tools in creating super-Gaussian random excitations for fatigue test. The major drawback of this method is that the magnitude distortion can be seen in both auto-power spectral density (ASD) and cross power-spectral density (CSD) of the excitation if the dynamic range of the target power spectral density (PSD) is large. To study the problem, we introduced Fourier series of a Gaussian signal into a cubic system, which is a common mathematical model shared by most of the ZMNL functions. We found that the cubic system produces a component leading to the distortion of both ASD and CSD. Meanwhile, if the shape of the reference ASD is flat in a frequency band, the distortion will not happen in the band. Based on this findings, a novel method is proposed in this article. It employs a pseudo reference PSD with flat ASDs to generate non-Gaussian signals in order to avoid the PSD distortions. Designed FIR filters are then applied to rescale the ASDs of the generated signals. After, iterative processes are introduced to recover the kurtoses of these filtered signals. The method is applied on a two-input and two-output numerical model, the feasibility and the availability of the method is verified. Finally, two control schemes based on the proposed pseudo reference PSD method are provided for a shaker table test. Test results show that both control schemes can eliminate the mismatch between the target PSD and the measured PSD of a shaker table.

Denoising method for Raman spectra with low signal-to-noise ratio based on feature extraction

Raman spectroscopy is a non-destructive technique utilizing lasers to observe scattered light in order to determine things such as vibrational modes in the molecular system. A major problem inherent to this technique is that due to their short exposure time and the low power of the excitation laser, Raman signals are very weak. They tend to be much weaker than the noise and can even be drowned out. Conventional denoising methods are currently unable to extract Raman peaks with precision so it is necessary to specifically study Raman signal extraction methods that involve a low signal-to-noise ratio (SNR). In this study, a denoising method for Raman spectra with low SNR based on feature extraction was proposed. Based on the Hilbert Vibration Decomposition (HVD) method, the Raman spectra was decomposed into two components. The peaks were located in the first component and compensated by those in the second component. Then based on the position and height of the peaks, their full widths at half maximum (FWHM) are calculated. Finally, based on the position, height and FWHM of the peaks, Gaussian signals are used to reconstruct the Raman peaks from strong noise and baseline. In the data simulation experiment, the denoising method used improved the SNR from 3.5316 to 130.6386 and the mean square error (MSE) was reduced from 213.8635 to 14.0404. In the actual experiment, this method successfully extracted the characteristic peaks of melamine despite the noise from employing a low excitation laser (10 mW). The characteristics such as the amplitude and position of the peaks were identical to those obtained under a high excitation laser (150 mW). The error of the FWHM under different excitation laser powers (10 and 150 mW) was less than the spectral resolution. Using the method proposed in this paper, the Raman signal of biological samples such as rice leaves were extracted from the raw spectrum, and information on the spectral peak position, amplitude and FWHM were obtained with clarity. The characteristic peaks of the carotene molecule, protein amide I, protein phenylalanine, nucleic acid cytosine, cellulose, DNA phosphodiester, RNA phosphodiester, D-glucose, α-D glucose, chlorophyll, lignin and cellulose were all accurate as well. The results from the simulation data and actual experiments show that a method based on feature extraction can effectively extract Raman peaks even when they are submerged in background noise. It should be noted that the practicality of this method lies in the fact that it requires few parameters and is simple to operate and implement.

Maximizing the Partial Decode-and-Forward Rate in the Gaussian MIMO Relay Channel

It is known that circularly symmetric Gaussian signals are the optimal input signals for the partial decode-and-forward (PDF) coding scheme in the Gaussian multiple-input multiple-output (MIMO) relay channel, but there is currently no method to find the optimal covariance matrices nor to compute the optimal achievable PDF rate since the optimization is a non-convex problem in its original formulation. In this paper, we show that it is possible to find a convex reformulation of the problem by means of an approximation and a primal decomposition. We derive an explicit solution for the inner problem as well as an explicit gradient for the outer problem, so that the efficient cutting-plane method can be applied for solving the outer problem. Based on these ingredients, we propose a convergent algorithm whose output is an approximation of the globally optimal solution along with a certificate of accuracy in terms of a maximum distance to the true global optimum. In numerical simulations, this distance converged to values close to zero in all considered instances of the problem, showing that the proposed method manages to find the global optimum in all these instances.

Blind Direction-of-Arrival Estimation in Acoustic Vector-Sensor Arrays via Tensor Decomposition and Kullback-Leibler Divergence Covariance Fitting

A blind Direction-of-Arrivals (DOAs) estimate of narrowband signals for Acoustic Vector-Sensor (AVS) arrays is proposed. Building upon the special structure of the signal measured by an AVS, we show that the covariance matrix of all the received signals from the array admits a natural low-rank 4-way tensor representation. Thus, rather than estimating the DOAs directly from the raw data, our estimate arises from the unique parametric Canonical Polyadic Decomposition (CPD) of the observations' Second-Order Statistics (SOSs) tensor. By exploiting results from fundamental statistics and the recently re-emerging tensor theory, we derive a consistent blind CPD-based DOAs estimate without prior assumptions on the array configuration. We show that this estimate is a solution to an equivalent approximate joint diagonalization problem, and propose an ad-hoc iterative solution. Additionally, we derive the Cram\'er-Rao lower bound for Gaussian signals, and use it to derive the iterative Fisher scoring algorithm for the computation of the Maximum Likelihood Estimate (MLE) in this particular signal model. We then show that the MLE for the Gaussian model can in fact be used to obtain improved DOAs estimates for non-Gaussian signals as well (under mild conditions), which are optimal under the Kullback-Leibler divergence covariance fitting criterion, harnessing additional information encapsulated in the SOSs. Our analytical results are corroborated by simulation experiments in various scenarios, which also demonstrate the considerable improved accuracy w.r.t. a competing state-of-the-art blind estimate for AVS arrays, reducing the resulting root mean squared error by up to more than an order of magnitude.

On Energy-Information Balance in Automatic Control Systems Revisited.

We revise and slightly generalize some variational problems related to the “informational approach” in the classical optimization problem for automatic control systems which was popular from 1970–1990. We find extremals for various degenerated (derivative independent) functionals and propose some interpretations of obtained minimax relations. The main example of such functionals is given by the Gelfand–Pinsker–Yaglom formula for the information quantity contained in one random process in another one. We find some balance relations in a linear stationary one-dimensional system with Gaussian signal and interpret them in terms of Legendre duality.

Multifunctional holographic gratings for simultaneous coupling and beam splitting applications in photonic integrated circuits

A novel holographic grating for simultaneous coupling of power and optical beam splitting application is designed. The proposed design incorporates two identical holo-gratings separated by a distance D. A microscopic object such as micro-sphere or micro-ring is introduced in between these two gratings at a distance $$ \frac{D}{2} $$ and a Gaussian signal is allowed to pass through the first holo-grating which emerges out of the second one. With the proposed design eleven different splitting ratios could be achieved successfully by varying dimension of microscopic objects and the orientations of holo-gratings with respect to plane of incidence. For coupling applications the simulation of the proposed design shows 100% Transmission Efficiency (TE). This leads to an immense flexibility for the use of proposed model in Photonic Integrated Circuits. We demonstrate the possibility of such a multi-functional Holographic device with the aid of Finite Difference Time Domain (FDTD) simulations. To the best of our knowledge, this is the first investigation where simultaneous beam splitting and coupling applications are realized in a holographic optical element.

Investigation on soliton mode-locked fiber laser with PbSe quantum dot as gain medium by numerical simulation

A soliton mode-locked lead selenide (PbSe) quantum-dot-doped fiber laser (QDFL) is proposed and investigated by numerical simulation for the first time. Buildup dynamics in time and spectral domains are studied. Output properties starting from Gaussian and noise-like signals are characterized. The optimum quantum-dot-doped fiber lengths are revealed under various PbSe quantum dot doping concentrations. The evolutions of the pulse and spectrum in the resonator at the steady state are discussed. The results obtained facilitate the understanding of the operating principle of QDFL for solving emission wavelength problem.

Assessing the detectability of a stochastic gravitational wave background with LISA, using an excess of power approach

The laser interferometer space antenna will be the first gravitational wave observatory in space. It is scheduled to fly in the early 2030’s. LISA design predicts sensitivity levels that potentially enable the detection a stochastic gravitational wave background signal. This stochastic type of signal is a superposition of signatures from sources that cannot be resolved individually and which are of various types, each one contributing with a different spectral shape. In this work we present a fast methodology to assess the detectability of a stationary, Gaussian, and isotropic stochastic signal in a set of frequency bins, combining information from the available data channels. We derive an analytic expression of the Bayes factor between the instrumental noise-only and the signal plus instrumental noise models, that allows us to compute the detectability bounds of a given signal, as a function of frequency and prior knowledge on the instrumental noise spectrum.

Bank Coordination and Monetary Transmission: Evidence from India

We propose a new channel for the transmission of monetary policy shocks, the coordination channel. We develop a New Keynesian model in which bank lending is strategically complementary. Banks do not observe the distribution of loans but infer it using Gaussian signals. Under this paradigm, expectations of tighter credit conditions reduce banks’ lending response to monetary shocks. As a result, lack of coordination and information about other banks’ actions dampen monetary transmission. We test these predictions by constructing a dataset that links the evolution of interest rates to firms’ bank credit relationships in India. Consistent with our model, we find that the cross-sectional mean and dispersion of lending rates, which capture the expected value and the precision of the signals of credit extended by other banks, are significant predictors of monetary transmission. Our quantitative results suggest that lending complementarities reduce monetary transmission to inflation and output by about a third.

Maximum Likelihood Decoding for Channels With Gaussian Noise and Signal Dependent Offset

In many channels, the transmitted signals do not only face noise, but offset mismatch as well. In the prior art, maximum likelihood (ML) decision criteria have already been developed for noisy channels suffering from signal independent offset . In this paper, such ML criterion is considered for the case of binary signals suffering from Gaussian noise and signal dependent offset . The signal dependency of the offset signifies that it may differ for distinct signal levels, i.e., the offset experienced by the zeroes in a transmitted codeword is not necessarily the same as the offset for the ones. Besides the ML criterion itself, also an option to reduce the complexity is considered. Further, a brief performance analysis is provided, confirming the superiority of the newly developed ML decoder over classical decoders based on the Euclidean or Pearson distances.

Bayesian step least mean squares algorithm for Gaussian signals

Selecting the step of the least mean squares (LMS) algorithm is an old problem. This study uses a new approach to address this problem resulting in a new algorithm with excellent system identification performance. The LMS algorithm, with time-varying step, size can be shown to be equivalent to the Kalman filter in some conditions. This is as long as the state noise of the Kalman filter and the step size of the LMS algorithm are chosen carefully. The Kalman filter is the optimum linear estimator (Bayesian) given the state and the measurement noise covariance matrices, but these matrices are not always known. This work considers the case where these matrices are not known, in the special cases that the Kalman filter reduces to the LMS. This results in an algorithm to select the step-size of the LMS algorithm with few priors. The optimum step size can be calculated using estimates of the probability density function (PDF) of the coefficient estimation error variance (qw ) and measurement noise variance (qv ). The PDFs can be estimated from the data using Bayes’ rule and assuming Gaussian reference and measurement noise signals. The resulting algorithm to determine qw and qv is a second small Kalman filter, and the outputs of this filter (means and covariances) are used to determine the expected value of the step.