Necessary Number Of Samples Research Articles

Choosing optimal input and sampling frequencies for analog to digital converter testing

The main objective of this paper is to study of the ideal input and sampling frequencies, as well as determining the necessary number of samples for achieving coherent sampling. This aspect holds significant importance when it comes to testing analog-to-digital converters (ADCs) using various techniques such as the Histogram Test Method, Discrete Fourier Transform Method, or Sine-Fitting Method. The study conducted in this paper sheds light on a crucial consideration, which is the trade-off between testing duration and the proximity to the required frequencies. This trade-off is determined by the number of acquired samples. The balance between the amount of time spent on testing and the accuracy achieved in terms of the frequencies being targeted is of great importance. By exploring the ideal input and sampling frequencies, along with the determination of the necessary number of samples for coherent sampling, this research contributes to enhancing the understanding of ADC testing methodologies. It provides valuable information for researchers and practitioners in the field, enabling them to make informed decisions regarding the selection of appropriate testing techniques and algorithms based on their specific requirements and constraints. Ultimately, the findings presented in this paper have the potential to improve the efficiency and effectiveness of ADC testing processes, leading to more accurate and reliable results.

CAD-Based Design Optimization of Four-Bar Mechanisms: An Emergency Ventilator Case Study

The design optimization of mechanisms is promising as it results in more energy-efficient machines without compromising performance. However, machine builders do not apply state-of-the-art methods, as these algorithms require case-specific theoretical analysis. Moreover, the design synthesis approaches in the literature predominantly utilize heuristic optimizers, leading to suboptimal local minima. This paper introduces a widely applicable workflow, guaranteeing the global optimum. The constraints describing the feasible region of the possible designs are essential to find the global optimum. Therefore, kinematic analysis of the point-to-point planar four-bar mechanism is discussed. Within the feasible design space, objective value samples were generated through the CAD multi-body software. These motion simulations determine the required torque to fulfill the movement for a combination of design parameters. This replaces the cumbersome analytic derivation of the torque. This paper introduces sparse interpolation techniques to avoid brute force sampling of the design space. The advantage of this approach is that it is easily scalable to more design parameters, as the interpolation method minimizes the number of necessary samples. This paper explains the mathematical background of our developed interpolation approach. However, a step-by-step procedure is introduced to allow the employment of the interpolation technique by machine designers without the necessity to understand the underlying mathematics. Finally, the mathematical expression, obtained from the interpolation, enables applying global optimizers. In a case study of an emergency ventilator mechanism with three design parameters, 1870 CAD motion simulations allowed reducing the RMS torque of the mechanism by 67%.

A Microwave Filter Yield Optimization Method Based on Off-Line Surrogate Model-Assisted Evolutionary Algorithm

Most existing microwave filter yield optimization methods target a small number of sensitive design variables (e.g., around 5). However, for many real-world cases, more than ten sensitive design variables need to be considered. Due to the complexity, yield optimization quality and efficiency become challenges. Hence, a new method, called yield optimization for filters based on the surrogate model-assisted evolutionary algorithm (YSMA), is proposed. The fundamental idea of YSMA is to construct a single high-accuracy surrogate model offline, which fully replaces electromagnetic (EM) simulations in the entire yield optimization process. Global optimization is then enabled to find designs with substantial yield improvement efficiently using the surrogate model. To reduce the number of necessary samples (i.e., EM simulations) while obtaining the required prediction accuracy, a customized machine learning technique is proposed. The performance of YSMA is demonstrated by two real-world examples with 11 and 14 design variables, respectively. Experimental results show the advantages of YSMA compared to the current dominant sequential online surrogate model-based local optimization methods.

Relationship of Teachers' Technology Skills and Selected Profile: Basis for Redesigning Training for Online Distance Learning Modality

The use of ICT as part of teacher’s instruction heightened because of the COVID-19 pandemic. This study analyzed the relationship of teacher’s selected profile such as educational attainment, field of specialization and years in service in association with skills in information processing, content creation, communication and problem-solving. The study utilized correlational research design and questionnaire as instrumentation. Simple random sampling was used to obtain the necessary number of samples from the population. Percentage and frequency distribution and chi-square test was used for analyzing the data collected. The data revealed in terms of content creation shows a significant relationship to educational attainment where it implies that the skills of making content using programs and software varies depending on the educational attainment a teacher achieved. Also, in terms of information processing, the data shows a significant relationship to years in service where it suggests that the skills in processing, collecting and analyzing information using online software and engine varies depending on the experience of the teacher. This study recommends introducing and utilize a variety of technology options in training teachers and consider new and innovative learning methods in training them.

Adaptive Data-Driven Wideband Compressive Spectrum Sensing for Cognitive Radio Networks

This paper presents a novel adaptive wideband compressed spectrum sensing scheme for cognitive radio (CR) networks. Compared to the traditional CSSbased CR scenarios, the proposed approach reconstructs neither the received signal nor its spectrum during the compressed sensing procedure. On the contrary, a precise estimation of wide spectrum support is recovered with a fewer number of compressed measurements. Then, the spectrum occupancy is determined directly from the reconstructed support vector. To carry out this process, a data-driven methodology is utilized to obtain the minimum number of necessary samples required for support reconstruction, and a closed-form expression is obtained that optimally estimates the number of desired samples as a function of the sparsity level and number of channels. Following this phase, an adjustable sequential framework is developed where the first step predicts the optimal number of compressed measurements and the second step recovers the sparse support and makes sensing decision. Theoretical analysis and numerical simulations demonstrate the improvement achieved with the proposed algorithm to significantly reduce both sampling costs and average sensing time without any deterioration in detection performance. Furthermore, the remainder of the sensing time can be employed by secondary users for data transmission, thus leading to the enhancement of the total throughput of the CR network.

Fully Decomposable Compressive Sampling With Joint Optimization for Multidimensional Sparse Representation

Conventional compressive sampling methods cannot efficiently exploit structured sparsity for sampling multidimensional signals like video sequences. In this paper, we propose a fully decomposable compressive sampling model that adopts the Kronecker product framework to exploit the structured sparsity spanning multidimensional signals. It enables efficient sampling in a progressive fashion by retaining the block-diagonal feature of Kronecker products. A synthetic sensing matrix is developed for joint optimization over sampling signals with multiple dimensions. Instead of adjusting global Gram matrix, separable minimization of mutual coherence in multiple dimensions is jointly formulated for a stable recovery with enhanced convergence rate. Sampling rate allocation is considered to improve recovery performance based on the decomposable compressive sampling. The proposed model is employed in video acquisition for temporal sparsity along motion trajectory. Experiment results show that the proposed model can improve the recovery performance with a reduced number of necessary samples in comparison to the state-of-the-art methods.

Features in constructing a certificate of strength of extraterrestrial material by the example of the Chelyabinsk meteorite

The mechanical properties of various components of the Chelyabinsk meteorite are studied. A measurement technique allowing one to obtain a strength certificate of the material by a minimum necessary number of samples with allowance for defectiveness is developed. Universal expressions for the chondritic component and impact melting have been obtained. The expressions allow one to make general estimates of the strength boundaries for LL type meteorites.

Automatic Frequency Identification under Sample Loss in Sinusoidal Pulse Width Modulation Signals Using an Iterative Autocorrelation Algorithm

In this work, we present a simple algorithm to calculate automatically the Fourier spectrum of a Sinusoidal Pulse Width Modulation Signal (SPWM). Modulated voltage signals of this kind are used in industry by speed drives to vary the speed of alternating current motors while maintaining a smooth torque. Nevertheless, the SPWM technique produces undesired harmonics, which yield stator heating and power losses. By monitoring these signals without human interaction, it is possible to identify the harmonic content of SPWM signals in a fast and continuous manner. The algorithm is based in the autocorrelation function, commonly used in radar and voice signal processing. Taking advantage of the symmetry properties of the autocorrelation, the algorithm is capable of estimating half of the period of the fundamental frequency; thus, allowing one to estimate the necessary number of samples to produce an accurate Fourier spectrum. To deal with the loss of samples, i.e., the scan backlog, the algorithm iteratively acquires and trims the discrete sequence of samples until the required number of samples reaches a stable value. The simulation shows that the algorithm is not affected by either the magnitude of the switching pulses or the acquisition noise.

405nm versus 633nm for protoporphyrin IX excitation in fluorescence-guided stereotactic biopsy of brain tumors.

Fluorescence diagnosis may be used to improve the safety and reliability of stereotactic brain tumor biopsies using biopsy needles with integrated fiber optics. Based on 5-aminolevulinic-acid-induced protoporphyrin IX (PpIX) fluorescence, vital tumor tissue can be localized in vivo during the excision procedure to reduce the number of necessary samples for a reliable diagnosis. In this study, the practical suitability of two different PpIX excitation wavelengths (405nm, 633nm) was investigated on optical phantoms. Violet excitation at 405nm provides a 50-fold higher sensitivity for the bulk tumor; this factor increases up to 100 with decreasing fluorescent volume as shown by ray tracing simulations. Red excitation at 633nm, however, is noticeably superior with regard to blood layers obscuring the fluorescence. Experimental results on the signal attenuation through blood layers of well-defined thicknesses could be confirmed by ray tracing simulations. Typical interstitial fiber probe measurements were mimicked on agarose-gel phantoms. Even in direct contact, blood layers of 20-40µm between probe and tissue must be expected, obscuring 405-nm-excited PpIX fluorescence almost completely, but reducing the 633-nm-excited signal only by 25.5%. Thus, 633nm seems to be the wavelength of choice for PpIX-assisted detection of high-grade gliomas in stereotactic biopsy. PpIX signal attenuation through clinically relevant blood layers for 405 nm (violet) and 633 nm (red) excitation.

Representative input load of antibiotics to WWTPs: Predictive accuracy and determination of a required sampling quantity

Predicting the input loads of antibiotics to wastewater treatment plants (WWTP) using certain input data (e.g. prescriptions) is a reasonable method if no analytical data is available. Besides the spatiotemporal uncertainties of the projection itself, only a few studies exist to confirm the suitability of required excretion data from literature. Prescription data with a comparatively high resolution and a sampling campaign covering 15 months were used to answer the question of applicability of the prediction approach. As a result, macrolides, sulfamethoxazole and trimethoprim were almost fully recovered close to 100% of the expected input loads. Nearly all substances of the beta-lactam family exhibit high elimination rates during the wastewater transport in the sewer system with a low recovery rate at the WWTP. The measured input loads of cefuroxime, ciprofloxacin and levofloxacin fluctuated greatly through the year which was not obvious from relatively constant prescribed amounts. The latter substances are an example that available data are not per se sufficient to monitor the actual release into the environment. Furthermore, the extensive data pool of this study was used to calculate the necessary number of samples to determine a representative annual mean load to the WWTP. For antibiotics with low seasonality and low input scattering a minimum of about 10 samples is required. In the case of antibiotics exhibiting fluctuating input loads 30 to 40 evenly distributed samples are necessary for a representative input determination. As a high level estimate, a minimum number of 20–40 samples per year is proposed to reasonably estimate a representative annual input load of antibiotics and other micropollutants.

연료전지 촉매층 내 촉매활성도에 대한 탄소지지 백금 촉매의 기하학적 비등방성 효과에 관한 연구

Transport phenomena of reactant and product are directly linked to intrinsic inhomogeneous random configurations of catalyst layer (CL) that consist of ionomer, carbon-supported catalyst (Pt/C), and pores. Hence, electrochemically active surface area (ECSA) of Pt/C is dominated by geometrical morphology of mass transport path. Undoubtedly these ECSAs are key factor of total fuel cell efficiency. In this study, non-deterministic micro-scale CLs were randomly generated by Monte Carlo method and implemented with the percolation process. To ensure valid inference about Pt/C catalyst utilization, 600 samples were chosen as the number of necessary samples with 95% confidence level. Statistic results of 600 samples generated under particular condition (20vol% Pt/C, 30vol% ionomer, 50vol% pore, and 20nm particle diameter) reveal only 18.2%~81.0% of Pt/C can construct ECSAs with mean value of 53.8%. This study indicates that the catalyst utilization in fuel cell CLs cannot be identical notwithstanding the same design condition.

Effects of the series length on Lempel-Ziv Complexity during sleep.

Lempel-Ziv Complexity (LZC) has been demonstrated to be a powerful complexity measure in several biomedical applications. During sleep, it is still not clear how many samples are required to ensure robustness of its estimate when computed on beat-to-beat interval series (RR). The aims of this study were: i) evaluation of the number of necessary samples in different sleep stages for a reliable estimation of LZC; ii) evaluation of the LZC when considering inter-subject variability; and iii) comparison between LZC and Sample Entropy (SampEn). Both synthetic and real data were employed. In particular, synthetic RR signals were generated by means of AR models fitted on real data. The minimum number of samples required by LZC for having no changes in its average value, for both NREM and REM sleep periods, was 10(4) (p<;0.01) when using a binary quantization. However, LZC can be computed with N >1000 when a tolerance of 5% is considered satisfying. The influence of the inter-subject variability on the LZC was first assessed on model generated data confirming what found (>10(4); p<;0.01) for both NREM and REM stage. However, on real data, without differentiate between sleep stages, the minimum number of samples required was 1.8×10(4). The linear correlation between LZC and SampEn was computed on a synthetic dataset. We obtained a correlation higher than 0.75 (p<;0.01) when considering sleep stages separately, and higher than 0.90 (p<;0.01) when stages were not differentiated. Summarizing, we suggest to use LZC with the binary quantization and at least 1000 samples when a variation smaller than 5% is considered satisfying, or at least 10(4) for maximal accuracy. The use of more than 2 levels of quantization is not recommended.

Real-time rendering of glossy materials with regular sampling

Rendering view-dependent, glossy surfaces to increase the realism in real-time applications is a computationally complex task, that can only be performed by applying some approximations--especially when immediate changes in the scene in terms of material settings and object placement are a necessity. The use of environment maps is a common approach to this problem, but implicates performance problems due to costly pre-filtering steps or expensive sampling. We, therefore, introduce a regular sampling scheme for environment maps that relies on an efficient MIP-map-based filtering step, and minimizes the number of necessary samples for creating a convincing real-time rendering of glossy BRDF materials.

An estimate of the truncation error in the asynchronous sampling of ac signals containing inter- and subharmonics

The estimation of the truncation error in the asynchronous sampling of an ac signal containing sub- and interharmonic components is considered. The expressions derived enable one to choose the optimum method and the necessary number of samples of a complex input signal. The limits of the error of the method of signal processing are determined taking the effect of sampling into account. Mathematical modeling of the procedure for estimating the possible truncation error is carried out.

Optimized Projection Matrix for Compressive Sensing

Compressive sensing (CS) is mainly concerned with low-coherence pairs, since the number of samples needed to recover the signal is proportional to the mutual coherence between projection matrix and sparsifying matrix. Until now, papers on CS always assume the projection matrix to be a random matrix. In this paper, aiming at minimizing the mutual coherence, a method is proposed to optimize the projection matrix. This method is based on equiangular tight frame (ETF) design because an ETF has minimum coherence. It is impossible to solve the problem exactly because of the complexity. Therefore, an alternating minimization type method is used to find a feasible solution. The optimally designed projection matrix can further reduce the necessary number of samples for recovery or improve the recovery accuracy. The proposed method demonstrates better performance than conventional optimization methods, which brings benefits to both basis pursuit and orthogonal matching pursuit.

Determination of the Truncation Errors in Case of Asynchronous Processing of the AC Signals in the Presence of Interharmonics and Subharmonics

The paper deals with the problem of estimating the influence of truncation error in case of asynchronous sampling of the ac signal in the presence of subharmonics and interharmonics. The analysis makes use of the most general model of the voltage and current signal, i.e. the most complex spectral content that can be expected to appear in practice. In this paper, different processing methods are compared end equations derived for worst-case errors. A simulations and experimental check of the suggested procedure have been done as well. On the base of the derived relation it is possible to select, the best processing method and select the necessary number of samples in case of such a complex signal. The paper investigates the errors related to the proposed processing method, and provides estimation of truncation affect.

Learning to Sense Sparse Signals: Simultaneous Sensing Matrix and Sparsifying Dictionary Optimization

Sparse signal representation, analysis, and sensing have received a lot of attention in recent years from the signal processing, optimization, and learning communities. On one hand, learning overcomplete dictionaries that facilitate a sparse representation of the data as a liner combination of a few atoms from such dictionary leads to state-of-the-art results in image and video restoration and classification. On the other hand, the framework of compressed sensing (CS) has shown that sparse signals can be recovered from far less samples than those required by the classical Shannon-Nyquist Theorem. The samples used in CS correspond to linear projections obtained by a sensing projection matrix. It has been shown that, for example, a nonadaptive random sampling matrix satisfies the fundamental theoretical requirements of CS, enjoying the additional benefit of universality. On the other hand, a projection sensing matrix that is optimally designed for a certain class of signals can further improve the reconstruction accuracy or further reduce the necessary number of samples. In this paper, we introduce a framework for the joint design and optimization, from a set of training images, of the nonparametric dictionary and the sensing matrix. We show that this joint optimization outperforms both the use of random sensing matrices and those matrices that are optimized independently of the learning of the dictionary. Particular cases of the proposed framework include the optimization of the sensing matrix for a given dictionary as well as the optimization of the dictionary for a predefined sensing environment. The presentation of the framework and its efficient numerical optimization is complemented with numerous examples on classical image datasets.

Evaluation of a core sampling scheme to characterize root length density of maize

Information about root distribution is important for characterization and modeling of water and nutrient uptake, biomass, and yield. Due to the heterogeneous distribution of roots in row crops, the reliability and representativeness of estimates of RL and root morphology using core sampling depend on the number of samples and their location. The objectives of this study were to evaluate errors when assessing RLD and root morphology from auger core sampling schemes, to estimate 2D distributions of RLD by auger core sampling, and to assess the number of samples necessary for representative estimates of RLD and RD classes. The reference dataset utilized in this study is based on completely sampled 3D soil monoliths under maize, taken at three different dates (55, 78, and 104 days after planting) and two different row spacings (75 and 37.5 cm). A hypothetical auger core sampling scheme with one core within the row and another midway between rows mostly overpredicted total RLD. Bias was lower when using an 1:3 weighting scheme. Estimation of 2D vertical RLD distribution by calculating the ratio of RLD in the plant row to RLD midway between rows yielded reasonable estimates only when the average of eight cores was used. An assessment of the proportions of RD classes yielded high bias values, even when using the average of eight cores. An analysis of sampling errors using successively more cores revealed that for total RLD, to attain a bias <20%, more than ten samples would be necessary. This suggests that the number of core samples taken in many root studies could be too low. This bias was even higher when taking core samples for estimation of proportions of RD classes, where a reasonably low bias between estimated and “true” values could not be attained in this study even with ten core samples. Consequently, when taking samples for measurement of root morphological parameters, more detailed and site-adapted sampling schemes have to be devised. For estimating total averaged RLD, two core samples (within-row and midway between rows) could be sufficient when using a 1:3 weighting scheme for calculating the average RLD. When samples are taken in a more random manner and no weighting is applied, the necessary number of samples would be at least ten.

Exact image reconstruction from a limited number of projections

A new method for the exact reconstruction of any gray-scale image from its projections is proposed. The original image is projected into several view angles and the projection samples are stored in an accumulator array. In order to reconstruct the image, the accumulator array is considered as an accumulation of sinusoidal contributions each one corresponding to a certain pixel of the original image. The proposed method defines conditions for the necessary number of projections and the density of ray samples on the projection axis. These conditions insure that, for each pixel, there is at least one sample in the accumulator array where only this particular pixel contributes. This characteristic projection sample is used during the reconstruction phase to determine the coordinates and the gray-scale value of the corresponding image pixel. A variation of the method is also proposed where the reconstruction is performed using a limited number of projection samples in certain view angles. Specifically, the number of necessary samples equals at most the overall number of pixels in the original image. This approach leads to a significant reduction of memory and processing time requirements since it provides exact image reconstruction using one projection sample per pixel.

The small ball punch test at FZJ

The next generation of nuclear power reactors and neutron sources, together with the test devices for the fusion program, will pose an unprecedented severity of the environment for structural components near the irradiation sources. Therefore there is a need for material development and testing in the anticipated conditions and a number of institutions are involved in the process. A strong constraint in the volume of material available for testing, due to the high irradiation dose needed to meet proper conditions and the number of necessary samples, has driven the development of a number of tests to extract engineering properties from miniaturised specimens [G.E. Lucas, Metall. Trans. A 21 (1990) 1105, P. Jung, A. Hishinuma, G.E. Lucas, H. Ullmaier, J. Nucl. Mater. 232 (1996) 186]. The small ball punch (BP) test is a mechanical test for miniaturised samples. Although it is not yet a standard test, specimens discs dimensions of 3 mm diameter and 250 μm thickness are routinely used. The BP test finds application in the determination of elastoplastic and fracture properties of materials, such as the tensile strength, yield strength, fracture energy and ductile to brittle transition temperature (DBTT). Here a BP test apparatus developed at the Forschungszentrum Jülich with the contribution of the INFM is presented and its performance discussed.