Double sampling derivatives and truncation error estimates

This paper investigates double sampling series derivatives for bivariate functions defined on R2 that are in the Bernstein space. For this sampling series, we estimate some of the pointwise and uniform bounds when the function satisfies some decay conditions. The truncated series of this formula allow us to approximate any order of partial derivatives for function from Bernstein space using only a finite number of samples from the function itself. This sampling formula will be useful in the approximation theory and its applications, especially after having the truncation error well-established. Examples with tables and figures are given at the end of the paper to illustrate the advantages of this formula.

Estimation of Mean in Double Sampling Using Exponential Technique on Multi-auxiliary Variates

This paper presents exponential-type ratio and product estimators for a finite population mean in double sampling using information on several auxiliary variates.The proposed estimators can be viewed as a generalization over the estimators suggested by Singh and Vishwakarma(Austrian J Stat 36(3):217–225,2007).The expressions for biases and mean square errors(MSEs)of the proposed estimators have been derived to the first degree of approximation.In addition,the expressions for minimum attainable MSEs are also investigated using the criterion for optimality of the weights.An empirical study is carried out in the support of the present study.Both theoretical andempirical findings are encouraging and support thesoundness that the proposed procedures for mean estimation perform better than the usual unbiased estimators and other well-known estimators under some realistic conditions.

A novel switched capacitor bandgap reference with a correlated double sampling structure

A switched capacitor bandgap voltage reference with correlated double sampling structure embedded in a temperature sensor is implemented in a standard 0.35 um CMOS process. Due to the smaller change of the op-amp＇s output voltage, this topology is very suitable for low power applications. In addition, errors caused by the finite op-amp gain, input offset voltage, and 1/f noise are eliminated with the correlated double sampling technique. Additionally, two-level process calibration techniques are designed to minimize the process spread. Finally, a method of getting a full period valid reference voltage output is discussed and experimental results are provided to verify the effectiveness of the proposed structure.

L-Moments Based Calibrated Variance Estimators Using Double Stratified Sampling

Variance is one of the most vital measures of dispersion widely employed in practical aspects.A commonly used approach for variance estimation is the traditional method of moments that is strongly influenced by the presence of extreme values,and thus its results cannot be relied on.Finding momentum from Koyuncu’s recent work,the present paper focuses first on proposing two classes of variance estimators based on linear moments(L-moments),and then employing them with auxiliary data under double stratified sampling to introduce a new class of calibration variance estimators using important properties of L-moments(L-location,L-cv,L-variance).Three populations are taken into account to assess the efficiency of the new estimators.The first and second populations are concerned with artificial data,and the third populations is concerned with real data.The percentage relative efficiency of the proposed estimators over existing ones is evaluated.In the presence of extreme values,our findings depict the superiority and high efficiency of the proposed classes over traditional classes.Hence,when auxiliary data is available along with extreme values,the proposed classes of estimators may be implemented in an extensive variety of sampling surveys.

Double Moving Extremes Ranked Set Sampling Design

The traditional simple random sampling(SRS)design method is inefficient in many cases.Statisticians proposed some new designs to increase efficiency.In this paper,as a variation of moving extremes ranked set sampling(MERSS),double MERSS(DMERSS)is proposed and its properties for estimating the population mean are considered.It turns out that,when the underlying distribution is symmetric,DMERSS gives unbiased estimators of the population mean.Also,it is found that DMERSS is more efficient than the SRS and MERSS methods for usual symmetric distributions(normal and uniform).For asymmetric distributions considered in this study,the DMERSS has a small bias and it is more efficient than SRS for usual asymmetric distribution(exponential)for small sample sizes.

An approximate point-based alternative for the estimation of variance under big BAF sampling

Background:A new variance estimator is derived and tested for big BAF(Basal Area Factor)sampling which is a forest inventory system that utilizes Bitterlich sampling(point sampling)with two BAF sizes,a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation.Methods:The new estimator is derived using the Delta method from an existing formulation of the big BAF estimator as consisting of three sample means.The new formula is compared to existing big BAF estimators including a popular estimator based on Bruce’s formula.Results:Several computer simulation studies were conducted comparing the new variance estimator to all known variance estimators for big BAF currently in the forest inventory literature.In simulations the new estimator performed well and comparably to existing variance formulas.Conclusions:A possible advantage of the new estimator is that it does not require the assumption of negligible correlation between basal area counts on the small BAF factor and volume-basal area ratios based on the large BAF factor selection trees,an assumption required by all previous big BAF variance estimation formulas.Although this correlation was negligible on the simulation stands used in this study,it is conceivable that the correlation could be significant in some forest types,such as those in which the DBH-height relationship can be affected substantially by density perhaps through competition.We derived a formula that can be used to estimate the covariance between estimates of mean basal area and the ratio of estimates of mean volume and mean basal area.We also mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of 1n where n is the number of sample points.

A note on the estimation of variance for big BAF sampling

Background:The double sampling method known as“big BAF sampling”has been advocated as a way to reduce sampling effort while still maintaining a reasonably precise estimate of volume.A well-known method for variance determination,Bruce’s method,is customarily used because the volume estimator takes the form of a product of random variables.However,the genesis of Bruce’s method is not known to most foresters who use the method in practice.Methods:We establish that the Taylor series approximation known as the Delta method provides a plausible explanation for the origins of Bruce’s method.Simulations were conducted on two different tree populations to ascertain the similarities of the Delta method to the exact variance of a product.Additionally,two alternative estimators for the variance of individual tree volume-basal area ratios,which are part of the estimation process,were compared within the overall variance estimation procedure.Results:The simulation results demonstrate that Bruce’s method provides a robust method for estimating the variance of inventories conducted with the big BAF method.The simulations also demonstrate that the variance of the mean volume-basal area ratios can be computed using either the usual sample variance of the mean or the ratio variance estimators with equal accuracy,which had not been shown previously for Big BAF sampling.Conclusions:A plausible explanation for the origins of Bruce’s method has been set forth both historically and mathematically in the Delta Method.In most settings,there is evidently no practical difference between applying the exact variance of a product or the Delta method—either can be used.A caution is articulated concerning the aggregation of tree-wise attributes into point-wise summaries in order to test the correlation between the two as a possible indicator of the need for further covariance augmentation.

CCD signal acquisition and optimal digital denoise technology

To reduce the charge-coupled device(CCD)readout noise and improve the detection ability under low illumination and dim targets,a new low-noise CCD signal processing technology-CCD digital denoiseis gradually being employed in aerospace detection and other fields.In this study,the main readout noise of CCD detectors and its characteristics are analyzed.A CCD digital denoise system and an experimental platform are designed as well as established by using a PCIe data acquisition card.According to the characteristics of readout noise,some digital filters are analyzed and designed based on distributed kernel coefficient,and the optimal kernel coefficients are obtained through iteration.Then,CCD signal and filter model are established,and the optimal filter is designed to apply to the digital denoise system.Finally,according to the image data obtained from the system,the performance of the digital denoise system and digital filtering algorithm is evaluated and compared.At 500 kHz and 1 MHz CCD readout rates,the denoising performance of the optimal filter designed in the experiment is 16%-32%higher than that of the digital filter with kernel distribution coefficient,and 50%-60%higher than that of the traditional correlated double sampling technology.

Live above-and belowground biomass of a Mozambican evergreen forest:a comparison of estimates based on regression equations and biomass expansion factors

Background： Biomass regression equations are claimed to yield the most accurate biomass estimates than biomass expansion factors （BEFs）. Yet, national and regional biomass estimates are generally calculated based on BEFs, especially when using national forest inventory data. Comparison of regression equations based and BEF-based biomass estimates are scarce. Thus, this study was intended to compare these two commonly used methods for estimating tree and forest biomass with regard to errors and biases. Methods： The data were collected in 2012 and 2014. In 2012, a two-phase sampling design was used to fit tree component biomass regression models and determine tree BEFs. In 2014, additional trees were felled outside sampling plots to estimate the biases associated with regression equation based and BEF-based biomass estimates; those estimates were then compared in terms of the following sources of error： plot selection and variability, biomass model, model parameter estimates, and residual variability around model prediction. Results： The regression equation based below-, aboveground and whole tree biomass stocks were, approximately, 7.7, 8.5 and 8.3 % larger than the BEF-based ones. For the whole tree biomass stock, the percentage of the total error attributed to first phase （random plot selection and variability） was 90 and 88 % for regression- and BEF-based estimates, respectively, being the remaining attributed to biomass models （regression and BEF models, respectively）. The percent bias of regression equation based and BEF-based biomass estimates for the whole tree biomass stock were -2.7 and 5.4 %, respectively. The errors due to model parameter estimates, those due to residual variability around model prediction, and the percentage of the total error attributed to biomass model were larger for BEF models （than for regression models）, except for stem and stem wood components. Conclusions＂ The regression equation based biomass stocks were found to be slightly larger, associated with relatively smaller errors and least biased than the BEF-based ones. For stem and stem wood, the percentages of their total errors （as total variance） attributed to BEF model were considerably smaller than those attributed to biomass regression equations.

MIXED-GRAINED CMOS FIELD PROGRAMMABLE ANALOG ARRAY FOR SMART SENSORY APPLICATIONS

The drive towards shorter design cycles for analog integrated circuits has given impetus to the development of Field Programmable Analog Arrays(FPAAs),which are the analogue counterparts of Field Programmable Gate Arrays(FPGAs).In this paper,we present a new design methodology which using FPAA as a powerful analog front-end processing platform in the smart sensory microsystem.The proposed FPAA contains 16 homogeneous mixed-grained Configurable Analog Blocks(CABs) which house a variety of processing elements especially the proposed fine-grained Core Configurable Amplifiers(CCAs).The high flexible CABs allow the FPAA operating in both continuous-time and discrete-time approaches suitable to support variety of sensors.To reduce the nonideal parasitic effects and save area,the fat-tree interconnection network is adopted in this FPAA.The functionality of this FPAA is demonstrated through embedding of voltage and capacitive sensor signal readout circuits and a configurable band pass filter.The minimal detectable voltage and capacitor achieves 38 uV and 8.3 aF respectively within 100 Hz sensor bandwidth.The power consumption comparison of CCA in three applications shows that the FPAA has high power efficiency.And the simulation results also show that the FPAA has good tolerance with wide PVT variations.

A low-power high-quality CMOS image sensor using 1.5 V 4T pinned photodiode and dual-CDS column-parallel single-slope ADC

This paper presents a low-power high-quality CMOS image sensor(CIS)using 1.5 V 4T pinned photodiode(4T-PPD)and dual correlated double sampling(dual-CDS)column-parallel single-slope ADC.A five-finger shaped pixel layer is proposed to solve image lag caused by low-voltage 4T-PPD.Dual-CDS is used to reduce random noise and the nonuniformity between columns.Dual-mode counting method is proposed to improve circuit robustness.A prototype sensor was fabricated using a 0.11μm CMOS process.Measurement results show that the lag of the five-finger shaped pixel is reduced by 80%compared with the conventional rectangular pixel,the chip power consumption is only 36 mW,the dynamic range is 67.3 dB,the random noise is only 1.55 e^(-)_(rms),and the figure-of-merit is only 1.98 e^(-)·nJ,thus realizing low-power and high-quality imaging.

An A/D interface based on ∑△ modulator for thermal vacuum sensor ASICs

A newΣΔmodulator architecture for thermal vacuum sensor ASICs is proposed.The micro-hotplate thermal vacuum sensor fabricated by surface-micrornachining technology can detect the gas pressure from 1 to 10;Pa. The amplified differential output voltage signal of the sensor feeds to theΣΔmodulator to be converted into digital domain.The presentedΣΔmodulator makes use of a feed-forward path to suppress the harmonic distortions and attain high linearity.Compared with other feed-forward architectures presented before,the circuit complexity,chip area and power dissipation of the proposed architecture are significantly decreased.The correlated double sampling technique is introduced in the 1st integrator to reduce the flicker noise.The measurement results demonstrate that the modulator achieves an SNDR of 79.7 dB and a DR of 80 dB over a bandwidth of 7.8 kHz at a sampling rate of 4 MHz.The circuit has been fabricated in a 0.5μm 2P3M standard CMOS technology.It occupies an area of 5 mm;and dissipates 9 mW from a single 3 V power supply.The performance of the modulator meets the requirements of the considered application.

A 10-bit column-parallel cyclic ADC for high-speed CMOS image sensors

This paper presents a high-speed column-parallel cyclic analog-to-digital converter（ADC） for a CMOS image sensor.A correlated double sampling（CDS） circuit is integrated in the ADC,which avoids a stand-alone CDS circuit block.An offset cancellation technique is also introduced,which reduces the column fixed-pattern noise（FPN） effectively.One single channel ADC with an area less than 0.02 mm^2 was implemented in a 0.13μm CMOS image sensor process.The resolution of the proposed ADC is 10-bit,and the conversion rate is 1.6 MS/s. The measured differential nonlinearity and integral nonlinearity are 0.89 LSB and 6.2 LSB together with CDS, respectively.The power consumption from 3.3 V supply is only 0.66 mW.An array of 48 10-bit column-parallel cyclic ADCs was integrated into an array of CMOS image sensor pixels.The measured results indicated that the ADC circuit is suitable for high-speed CMOS image sensors.

A digital CDS technique and its performance testing

Readout noise is a critical parameter for characterizing the performance of charge-coupled devices（CCDs）, which can be greatly reduced by the correlated double sampling（CDS） circuit. However, a conventional CDS circuit inevitably introduces new noise since it consists of several active analog components such as operational amplifiers. This paper proposes a digital CDS circuit technique, which transforms the pre-amplified CCD signal into a train of digital presentations by a high-speed data acquisition card directly without the noisy CDS circuit,then implements the digital CDS algorithm through a numerical method. A readout noise of 3.3 e- and an energy resolution of 121 e V@5.9 ke V can be achieved via the digital CDS technique.

Research on high-speed TDICCD remote sensing camera video signal processing

Video signal processing needs high signal-to-noise ratio （SNR） in high-speed time delay and integration charge coupled devices （TDICCD）. To solve this problem, this article first analyzes the characteristics of the output video signal of a new type of high-speed TDICCD and its operation principle. Then it studies the correlation double sample （CDS） method of reducing noise. Following that a synthesized processing method is proposed, including correlation double sample, programmable gain control, line calibration and digital offset control, etc. Among the methods, XRD98L59 is a video signal processor for the charge coupled device （CCD）. Application of this processor to one kind of high-speed TDICCD with eight output ports achieves perfect video images. The experiment result indicates that the SNR of the images reaches about 50 dB. The video signal processing for high-speed multi-channel TDICCD is implemented, which meets the required project index.

Novel entropy estimators of a continuous random variable

This paper presents some novel entropy estimators of a continuous random variable using simple random sampling(SRS),ranked set sampling(RSS),and double RSS(DRSS)schemes.The theoretical results of the proposed entropy estimators are derived.The proposed entropy estimators are compared in terms of the bias and the root mean squared errors,theoretically and numerically,with the Vasicek O.[A test for normality based on sample entropy,J.R.Stat.Soc.B 38:54–59,1976.]entropy estimators using SRS,RSS,and DRSS schemes.It turns out that the new novel entropy estimators are substantially better than the existing Vasicek’s entropy estimators.