Sinusoidal Components Research Articles

The Predictability of a Target Signal Affects Manual Feedforward Control

In the manual control of a dynamic system, the human controller (HC) is often required to follow a visible and predictable reference path. Using the predictable aspect of a reference signal, through applying feedforward control, the HC can significantly improve performance as compared to a purely feedback control strategy. A proper definition of a signal’s predictability, however, is never given in literature. This paper investigates the predictability of a sum-of-sinusoids target signal, as a function of the number of sinusoid components and the fact whether the sinusoid frequencies are harmonic, or not. A human-in-the-loop experiment was done, with target signals varying for these two signal characteristics. A combined feedback-feedforward HC model was identified and parameters were estimated. It was found that for all experimental conditions, subjects used a feedforward strategy. Results further showed thatsubjects were able to perform better for harmonic signals as compared to non-harmonic signals, for signals with roughly the same frequency content.

Changes in Plasma Lipids during Exposure to Total Sleep Deprivation.

The effects of sleep loss on plasma lipids, which play an important role in energy homeostasis and signaling, have not been systematically examined. Our aim was to identify lipid species in plasma that increase or decrease reliably during exposure to total sleep deprivation. Twenty individuals underwent sleep deprivation in a laboratory setting. Blood was drawn every 4 h and mass spectrometry techniques were used to analyze concentrations of 263 lipid species in plasma, including glycerolipids, glycerophospholipids, sphingolipids, and sterols. Chronobiology and Sleep Laboratory, Duke-NUS Graduate Medical School. Healthy ethnic-Chinese males aged 21-28 y (n = 20). Subjects were kept awake for 40 consecutive hours. Each metabolite time series was modeled as a sum of sinusoidal (circadian) and linear components, and we assessed whether the slope of the linear component differed from zero. More than a third of all individually analyzed lipid profiles exhibited a circadian rhythm and/or a linear change in concentration during sleep deprivation. Twenty-five lipid species showed a linear and predominantly unidirectional trend in concentration levels that was consistent across participants. Choline plasmalogen levels decreased, whereas several phosphatidylcholine (PC) species and triacylglycerides (TAG) carrying polyunsaturated fatty acids increased. The decrease in choline plasmalogen levels during sleep deprivation is consistent with prior work demonstrating that these lipids are susceptible to degradation by oxidative stress. The increase in phosphatidylcholines and triacylglycerides suggests that sleep loss might modulate lipid metabolism, which has potential implications for metabolic health in individuals who do not achieve adequate sleep.

Phase‐locked loops redesign by the Lyapunov theory

A new approach is proposed to design a phase-locked loop (PLL) as an adaptive system in order to extract the desired sinusoidal component of the input signal, and estimate its amplitude and phase. In this method, the Lyapunov stability theorem is used to obtain adjustment rules for parameters, i.e. the stability of the system and convergence of the parameters are guaranteed in the sense of Lyapunov. Simulation results show the effectiveness of the proposed structure, and demonstrate that the input signal level and adaptation gains do not change the performance of the system. The proposed PLL structure can be utilised for fast and accurate applications in signal processing, power electronics, communication systems, and control.

Focused wave evolution using linear and second order wavemaker theory

In this paper, the evolution of focused waves using different paddle displacements (piston type) under laboratory conditions is presented. It is well known that in intermediate water depths, linear paddle displacements will generate spurious, free, sub and super harmonics. Thus, a second order correction to suppress these spurious free sub and super harmonics was used to generate the focused waves. The focused waves were generated in the laboratory using a linear superimposition principle, in which the wave paddle displacement is derived based on the sum of a number of sinusoidal components at discrete frequencies, whose phases are accordingly set to focus at a particular location. For this method of generation, the second order wave maker theory proposed by Schäffer [24] can be easily adopted and was used in the present study. Two different centre frequencies (fc=0.68Hz and 1.08Hz) with three different bandwidth ratios (Δf/fc=0.5, 0.75 and 1.0) were tested in a constant water depth, to consider both narrow and broadband spectra. These test cases correspond to wave focusing packets propagating in intermediate and deep water regions. Further, for each wave packet, two different amplitudes were considered in order to analyze non-breaking and breaking cases. Thus, by systematically generating the wave packets using the linear and second order paddle displacements, the analysis was carried out for the spectral and temporal evolution of selected long waves. The temporal evolution of the selected harmonics was analyzed using the Inverse Fast Fourier Transform (IFFT), to show the propagation of the spurious, free, long waves. Further, the variations in energy for the lower, higher and primary frequency ranges are reported for different wave paddle displacements. The analysis revealed that for the broadband spectrum the differences are more pronounced when using linear paddle displacements. We have also noticed a shift in focusing/breaking location and time (i.e. premature) due to the increase in crest height using linear displacements. The experiment data used in this paper has been provided as a supplementary, which can be used to validate the numerical models.

Estimating trend from seasonal data: is daily, monthly or annual data best?

We consider a model for time series whose mean has a component that is linear in time with slope b plus seasonal sinusoidal components. Suppose we have N years of observations and J observations per year. We answer the question: what is the loss in efficiency of estimating b if the J observations are grouped into weekly means, monthly means, annual means, and so on? We give answers for the cases of a single sinusoidal component and q sinusoidal components. We derive tests of hypotheses, confidence intervals, and power functions for the slope. Finally, an application of the results to daily minimum and daily maximum temperature data from Auckland is presented. Copyright © 2015 John Wiley & Sons, Ltd.

Simultaneous denoising and compression of power system disturbances using sparse representation on overcomplete hybrid dictionaries

This study introduces a novel unified framework for simultaneous denoising and compression of electric power system disturbance signals using sparse signal decomposition and reconstruction on overcomplete hybrid dictionary (OHD) matrix. In the proposed method, the power quality signal is first decomposed into deterministic sinusoidal components and non-deterministic components using the OHD matrix, including discrete impulse dictionary ( I ), cosine dictionary ( C ), sine dictionary ( S ) and the l1-norm optimisation algorithm. Then, the hard-thresholding, uniform threshold dead-zone quantisation, modified index coding and Huffman coding techniques are used for compression of significant detail signal samples and approximation coefficients. To justify the selection of OHD matrix, four compression methods are implemented using the decomposition techniques based on the dictionaries Ψ = [ I C S ] and Ψ = [ I C ], the wavelet transform (WT) and the discrete cosine transform (DCT). The performance of each method is tested and validated using a wide variety of typical power quality disturbance (PQD) signals taken from the IEEE-1159-PQE and GIM–PQE databases and generated using the Microgrid model. The results show that the method with dictionary Ψ = [ I C S ] is capable of effectively compressing the PQD signals as well as suppressing the noise components in the signals.

Comment on “Measurements of Newton's gravitational constant and the length of day” by Anderson J. D. et al.

There have been recent claims (Anderson et al., EPL, 110, 10002) of a 5.9 year periodicity in measurements of Newton's gravitational constant, $G$, which show a very strong correlation with observed periodic variations in the length of the day. I have used Bayesian model comparison to test this claim compared to other hypotheses that could explain the variation in the $G$ measurements. I have used the data from the initial claim, and from an updated set of compiled $G$ measurements that more accurately reflect the experimental dates, and find that a model containing an additional unknown Gaussian noise component is hugely favoured, by factors of $\gtrsim e^{30}$, over two models allowing for a sinusoidal component.

Graphics processing unit-assisted real-time three-dimensional measurement using speckle-embedded fringe.

This paper presents a novel two-frame fringe projection technique for real-time, accurate, and unambiguous three-dimensional (3D) measurement. One of the frames is a digital speckle pattern, and the other one is a composite image which is generated by fusing that speckle image with sinusoidal fringes. The contained sinusoidal component is used to obtain a wrapped phase map by Fourier transform profilometry, and the speckle image helps determine the fringe order for phase unwrapping. Compared with traditional methods, the proposed pattern scheme enables measurements of discontinuous surfaces with only two frames, greatly reducing the number of required patterns and thus reducing the sensitivity to movements. This merit makes the method very suitable for inspecting dynamic scenes. Moreover, it shows close performance in measurement accuracy compared with the phase-shifting method from our experiments. To process data in real time, a Compute Unified Device Architecture-enabled graphics processing unit is adopted to accelerate some time-consuming computations. With our system, measurements can be performed at 21 frames per second with a resolution of 307,000 points per frame.

Nonlocal response functions for predicting shear flow of strongly inhomogeneous fluids. II. Sinusoidally driven shear and multisinusoidal inhomogeneity.

We use molecular-dynamics computer simulations to investigate the density, strain-rate, and shear-pressure responses of a simple model atomic fluid to transverse and longitudinal external forces. We have previously introduced a response function formalism for describing the density, strain-rate, and shear-pressure profiles in an atomic fluid when it is perturbed by a combination of longitudinal and transverse external forces that are independent of time and have a simple sinusoidal spatial variation. In this paper, we extend the application of the previously introduced formalism to consider the case of a longitudinal force composed of multiple sinusoidal components in combination with a single-component sinusoidal transverse force. We find that additional harmonics are excited in the density, strain-rate, and shear-pressure profiles due to couplings between the force components. By analyzing the density, strain-rate, and shear-pressure profiles in Fourier space, we are able to evaluate the Fourier coefficients of the response functions, which now have additional components describing the coupling relationships. Having evaluated the Fourier coefficients of the response functions, we are then able to accurately predict the density, velocity, and shear-pressure profiles for fluids that are under the influence of a longitudinal force composed of two or three sinusoidal components combined with a single-component sinusoidal transverse force. We also find that in the case of a multisinusoidal longitudinal force, it is sufficient to include only pairwise couplings between different longitudinal force components. This means that it is unnecessary to include couplings between three or more force components in the case of a longitudinal force composed of many Fourier components, and this paves the way for a highly accurate but tractable treatment of nonlocal transport phenomena in fluids with density and strain-rate inhomogeneities on the molecular length scale.

Sound production in the tiger-tail seahorse Hippocampus comes: Insights into the sound producing mechanisms.

Acoustic signals of the tiger-tail seahorse (Hippocampus comes) during feeding were studied using wavelet transform analysis. The seahorse "click" appears to be a compounded sound, comprising three acoustic components that likely come from two sound producing mechanisms. The click sound begins with a low-frequency precursor signal, followed by a sudden high-frequency spike that decays quickly, and a final, low-frequency sinusoidal component. The first two components can, respectively, be traced to the sliding movement and forceful knock between the supraorbital bone and coronet bone of the cranium, while the third one (purr) although appearing to be initiated here is produced elsewhere. The seahorse also produces a growling sound when under duress. Growling is accompanied by the highest recorded vibration at the cheek indicating another sound producing mechanism here. The purr has the same low frequency as the growl; both are likely produced by the same structural mechanism. However, growl and purr are triggered and produced under different conditions, suggesting that such "vocalization" may have significance in communication between seahorses.

Prediction of the heat gain of external walls: An innovative approach for full-featured excitations based on the simplified method of Mackey-and-Wright

Abstract Nowadays, simulation tools are available for calculating the thermal loads of multiple rooms of buildings, for given inputs. However, due to inaccuracies or uncertainties in some of the input data (e.g., thermal properties, air infiltrations flow rates, building occupancy), the evaluated thermal load may represent no more than just an estimate of the actual thermal load of the spaces. Accordingly, in certain practical situations, simplified methods may offer a more reasonable trade-off between effort and results accuracy than advanced software. Hence, despite the advances in computing power over the last decades, simplified methods for the evaluation of thermal loads are still of great interest nowadays, for both the practicing engineer and the graduating student, since these can be readily implemented or developed in common computational-tools, like a spreadsheet. The method of Mackey and Wright (M&W) is a simplified method that upon values of the decrement factor and time lag of a wall (or roof) estimates the instantaneous rate of heat transfer through its indoor surface. It assumes cyclic behaviour and shows good accuracy when the excitation and response have matching shapes, but it involves non negligible error otherwise, for example, in the case of walls of high thermal inertia. The aim of this study is to develop a simplified procedure that considerably improves the accuracy of the M&W method, particularly for excitations that noticeably depart from the sinusoidal shape, while not introducing a need for an excessive volume of data or complexity in the production of results. In the first simplified procedure discussed in the paper, a full-featured excitation is decomposed into a Fourier series and then the wall’s thermal behaviour is reconstructed from the application of the M&W method to each of the N sinusoidal components. Even though this established approach can lead to the most accurate results, given a sufficiently high N , it requires the knowledge of the decrement factor and time lag associated to each component of the Fourier series, which can represent a considerable amount of data. The chief result of the research though is a novel procedure based on a parameter, γ , that weigh-averages the approximate solution obtained by considering a single term Fourier decomposition of the excitation and the solution by considering the actual excitation. The procedure is more accurate than the original M&W method and will be of interest to researchers with the means of generating values of γ for the walls which the end users of their research are interested in. It provides promising results for walls ranging from massive to negligible mass. It has been noticed that while using the same values of γ that had been optimized for the wall facing east, acceptable results are also obtained when altered external excitations are imposed, namely due to intermittency of the direct solar radiation or due to a distinct value of the external heat transfer coefficient.

A universal two-way approach for estimating unknown frequencies for unknown number of sinusoids in a signal based on eigenspace analysis of Hankel matrix

We develop a novel approach to estimate the \(n\) unknown constituent frequencies of a noiseless signal that comprises of unknown number, \(n\), of sinusoids of unknown phases and unknown amplitudes. The new two-way approach uses two constraints to accurately estimate the unknown frequencies of the sinusoidal components in a signal. The new approach serves as a verification test for the estimated unknown frequencies through the estimated count of the unknown number of frequencies. The Hankel matrix, of the time domain samples of the signal, is used as a basis for further analysis in the Pisarenko harmonic decomposition. The new constraints, the existence factor and the component factor, have been introduced in the methodology based on the relationships between the components of the sinusoidal signal and the eigenspace of the Hankel matrix. The performance of the developed approach has been tested to correctly estimate any number of frequencies within a signal with or without a fixed unknown bias. The method has also been tested to accurately estimate the very closely spaced low frequencies.

Optimal control based on a modified quadratic performance index for systems disturbed by sinusoidal signals

The problem of optimal control of systems disturbed by sinusoidal signals for infinite control time is considered. To evaluate the control laws, a modified mean-square performance index with an infinite control time was proposed. It is based on the proposed method for the decomposition of control signals on the interval from zero to infinity into the sum of sinusoidal components with selected frequencies and an additional auxiliary signal. The performance index was formulated in such a way that each sinusoidal component corresponds to a separate weight matrix. It was shown that there are infinitely many solutions for these optimization problems. Optimal control was selected in such a way that it should be independent of the state vector, and should depend only on the disturbance signal vector. The controller was synthesized for vibration reduction system. The paper presents results of numerical and laboratory studies of the designed vehicle active suspension system.

Model Order Selection for Complex Sinusoids in the Presence of Unknown Correlated Gaussian Noise

We consider the problem of detecting and estimating the amplitudes and frequencies of an unknown number of complex sinusoids based on noisy observations from an unstructured array. In parametric detection problems like this, information theoretic criteria such as minimum description length (MDL) and Akaike information criterion (AIC) have previously been used for joint detection and estimation. In our paper, model selection based on extreme value theory (EVT), which has previously been used for enumerating real sinusoidal components from one-dimensional observations, is generalized to the case of multidimensional complex observations in the presence of noise with an unknown spatial correlation matrix. Unlike the previous work, the likelihood ratios considered in the mutlidimensional case cannot be addressed using Gaussian random fields. Instead, chi-square random fields associated with the generalized likelihood ratio test are encountered and EVT is used to analyze the model order overestimation probability for a general class of likelihood penalty terms including MDL and AIC, and a novel likelihood penalty term derived based on EVT. Since the exact EVT penalty term involves a Lambert-W function, an approximate penalty term is also derived that is more tractable. We provide threshold signal-to-noise ratios (SNRs) and show that the model order underestimation probability is asymptotically vanishing for EVT and MDL. We also show that MDL and EVT are asymptotically consistent while AIC is not, and that with finite samples, the detection performance of EVT outperforms MDL and AIC. Finally, the accuracy of the derived threshold SNRs is also demonstrated.

FastMMD: Ensemble of Circular Discrepancy for Efficient Two-Sample Test

The maximum mean discrepancy (MMD) is a recently proposed test statistic for the two-sample test. Its quadratic time complexity, however, greatly hampers its availability to large-scale applications. To accelerate the MMD calculation, in this study we propose an efficient method called FastMMD. The core idea of FastMMD is to equivalently transform the MMD with shift-invariant kernels into the amplitude expectation of a linear combination of sinusoid components based on Bochner's theorem and Fourier transform (Rahimi & Recht, 2007). Taking advantage of sampling the Fourier transform, FastMMD decreases the time complexity for MMD calculation from O(N(2)d) to O(LN d), where N and d are the size and dimension of the sample set, respectively. Here, L is the number of basis functions for approximating kernels that determines the approximation accuracy. For kernels that are spherically invariant, the computation can be further accelerated to O(LN log d) by using the Fastfood technique (Le, Sarlós, & Smola, 2013). The uniform convergence of our method has also been theoretically proved in both unbiased and biased estimates. We also provide a geometric explanation for our method, ensemble of circular discrepancy, which helps us understand the insight of MMD and we hope will lead to more extensive metrics for assessing the two-sample test task. Experimental results substantiate that the accuracy of FastMMD is similar to that of MMD and with faster computation and lower variance than existing MMD approximation methods.

The Spectacular Rotation of Earth About the Main Axis

The fact that the orbit of Earth and the other planets in the Solar system are elliptic had been posing a mystery in science since creation. Also, explanation had been missing as to: the cause and the mysterious behavior of high and low tide as well as to the cause of Earth quakes. In this publication, it had been found that Earth rotates about the Main axis (alias the Geometric North-South axis) in a to-and-from motion with a period of about 365.24 days keeping the locus of its Obliquity fixed. All planets and natural satellites in the solar system are inclined to follow an elliptic trajectory because of the trait of the massive object in the gravitational relationship to exercise – by firing - a unilateral force, the robotics force, of decaying nature which causes the less massive partner not only to progressively change the plane of its trajectory but also causes the path of the less massive partner to be elliptic. The robotics force is responsible for the striking of quakes as well as for the happening and behavior of low and high tides. The robotics force will be represented by a sinusoidal component in the Newton’s law gravitation: The universe keeps an eye to its celestial objects by enforcing the law of the universe: .

MINIMAL SPARSE SAMPLING FOR FOURIER-POLYNOMIAL CHAOS IN ACOUSTIC SCATTERING

Single frequency acoustic scattering from an uncertain surface (with sinusoidal components) admits an efficient Fourier-polynomial chaos (FPC) expansion of the acoustic field. The expansion coefficients are computed nonintrusively, i.e., by functional sampling from existing acoustic models. The structure of the acoustic decomposition permits sparse selection of FPC orders within the framework of the Smolyak construction. The main result shows a minimal, sparse sampling required to exactly reconstruct FPC expansions of Smolyak form. To this end, this paper defines two concepts: exactly discretizable orthonormal, function systems (EDO); and nested systems created by decimation or “fledging.” An EDO generalizes the Nyquist-Shannon sampling conditions (exact recovery of “bandlimited” functions given sufficient sampling) to multidimensional FPC expansions. EDO criteria replace the concept of polynomially exact quadrature. Fledging parallels the idea of sub-sampling for sub-bands, from higher to lower level. The FPC Smolyak construction is an EDO fledged from a full grid EDO. An EDO results exactly when the sampled FPC expansion can be inverted to find its coefficients. EDO fledging requires that the lower level (1) has grid points and expansion orders nested in the higher level, and (2) derives its map from the samples to the coefficients from the higher level map. The theory begins with a single dimension fledged EDO, since a tensor product of fledged EDOs yields a fledged tensor EDO. A sequence of nested EDO levels fledge recursively from the largest EDO. The Smolyak construction uses telescoping sums of tensor products up to a maximum level to develop nested EDO systems for sparse grids and orders. The Smolyak construction transform gives exactly the inverse of the weighted evaluation map, and that inverse has a condition number that expresses the numerical limitations of the Smolyak construction.

Performance Comparison of Watermarking by Sorting and Without Sorting the Hybrid Wavelet Transforms Generated from Sinusoidal and Non-sinusoidal Orthogonal Transforms

In this paper a watermarking technique using hybrid wavelet transforms obtained from sinusoidal and non-sinusoidal component orthogonal transforms is proposed. Sinusoidal transform DCT and non-sinusoidal transforms Walsh, Haar and Discrete Kekre Transform are used to generate hybrid wavelet transforms namely DCT-Walsh, Walsh-DCT, DCT-Haar, Haar-DCT, DCT-DKT and DKT-DCT. Size of each component transform matrix is varied suitably from 4, 8, 16, 32, and 64 to generate hybrid wavelet transform matrix for host and watermark. The best size combination is further applied column wise and row wise to host and watermark and to embed the watermark middle frequency regions of host is selected. Embedding is first done without sorting the hybrid wavelet transform coefficients of host and watermark and then sorting is applied to observe the difference in the achieved robustness. Performance of proposed technique is evaluated against various attacks to decide whether sinusoidal transform when used as base transform matrix or local transform matrix is more robust.

Multi-pitch estimation exploiting block sparsity

We study the problem of estimating the fundamental frequencies of a signal containing multiple harmonically related sinusoidal components using a novel block sparse signal representation. An efficient algorithm for solving the resulting optimization problem is devised exploiting a novel variable step-size alternating direction method of multipliers (ADMM). The resulting algorithm has guaranteed convergence and shows notable robustness to the f0 vs f0/2 ambiguity problem. The superiority of the proposed method, as compared to earlier presented estimation techniques, is demonstrated using both simulated and measured audio signals, clearly indicating the preferable performance of the proposed technique.

An application of time-lag regression technique for assessment of groundwater fluctuations in a regulated river basin: a case study in Northeastern Thailand

Time series techniques have been applied to a wide variety of academic fields, particularly in the fields of economics, environment, and hydrology. This research work deals with application of the time-lag multiple linear regression technique to predicting the groundwater level and salinity fluctuation in a saline but irrigated area in Northeastern Thailand. Regulating gates are constructed to prevent flooding of the river downstream and to provide the surrounding upstream areas with sufficient irrigation water. The technique is essentially based on the lagged correlation between leading variables, i.e. rainfall and river stages, and their corresponding responses, i.e. groundwater depth and salinity. While the rainfall is simulated with a multiple sinusoidal model, the river stage model comprises two components: a single sinusoidal component and a multiple linear regression component implemented with independent variables, i.e. rainfall, regulating gate outflow, and irrigation supply. The shallow groundwater and groundwater salinity fluctuation in the irrigated area are shown by cross-correlation analysis to be dependent upon the surface water regulation and prior rainfall and thus can be simulated by a multiple linear regression with lagged time dependence. Once properly calibrated and verified, the model can perform better matching to the observed data vis-a-vis the conventional multiple linear regression model. The proposed model can also be deployed for forecasting and management of the future groundwater system, especially in situations in which costlier and more complex numerical modeling techniques are inapplicable.