Non-uniform Sampling Intervals Research Articles

Stability of Sampled-Data Systems With Packet Losses: A Nonuniform Sampling Interval Approach.

In this article, inspired by the Halanay inequality, we study stability of sampled-data systems with packet losses by proposing a nonuniform sampling interval approach. First, a sampled-data controller with an exponential gain is put forward to reduce conservatism. We obtain the sufficient condition for linear sampled-data systems to be exponentially stable by extending the famous Halanay inequality to sampled-data systems. The obtained sufficient conditions indicate that the maximal-allowable bound of sampling intervals is determined by the constant terms in the Halanay inequality, and the decay rate is presented in the form of a Lambert function. Compared with some existing results on the stability of sampled-data systems by using the Gronwall-Bellman Lemma, the conservatism induced by the exponential term via the Gronwall-Bellman Lemma can be reduced to some extent. Considering the phenomenon of packet losses, a new lemma is further proposed to generalize the proposed Halanay-like inequality. The results derived by the new lemma permit that there exist some sampling intervals with the upper bound violating the desired condition of the Halanay-like inequality. This permits us to establish exponential stability in significant cases that do not satisfy the Halanay-like inequality needed in the previous results. Finally, the sampled-data local exponential stability is investigated for nonlinear systems with strong nonlinearity.

Improvement of Distance Measurement Based on Dispersive Interferometry Using Femtosecond Optical Frequency Comb.

Since the dispersive interferometry (DPI) based on optical frequency combs (OFCs) was proposed, it has been widely used in absolute distance measurements with long-distance and high precision. However, it has a serious problem for the traditional DPI based on the mode-locked OFC. The error of measurements caused by using the fast Fourier transform (FFT) algorithm to process signals cannot be overcome, which is due to the non-uniform sampling intervals in the frequency domain of spectrometers. Therefore, in this paper, we propose a new mathematical model with a simple form of OFC to simulate and analyze various properties of the OFC and the principle of DPI. Moreover, we carry out an experimental verification, in which we adopt the Lomb–Scargle algorithm to improve the accuracy of measurements of DPI. The results show that the Lomb–Scargle algorithm can effectively reduce the error caused by the resolution, and the error of absolute distance measurement is less than 12 μm in the distance of 70 m based on the mode-locked OFC.

Robust identification of temporal biomarkers in longitudinal omics studies.

MotivationLongitudinal studies increasingly collect rich ‘omics’ data sampled frequently over time and across large cohorts to capture dynamic health fluctuations and disease transitions. However, the generation of longitudinal omics data has preceded the development of analysis tools that can efficiently extract insights from such data. In particular, there is a need for statistical frameworks that can identify not only which omics features are differentially regulated between groups but also over what time intervals. Additionally, longitudinal omics data may have inconsistencies, including non-uniform sampling intervals, missing data points, subject dropout and differing numbers of samples per subject.ResultsIn this work, we developed OmicsLonDA, a statistical method that provides robust identification of time intervals of temporal omics biomarkers. OmicsLonDA is based on a semi-parametric approach, in which we use smoothing splines to model longitudinal data and infer significant time intervals of omics features based on an empirical distribution constructed through a permutation procedure. We benchmarked OmicsLonDA on five simulated datasets with diverse temporal patterns, and the method showed specificity greater than 0.99 and sensitivity greater than 0.87. Applying OmicsLonDA to the iPOP cohort revealed temporal patterns of genes, proteins, metabolites and microbes that are differentially regulated in male versus female subjects following a respiratory infection. In addition, we applied OmicsLonDA to a longitudinal multi-omics dataset of pregnant women with and without preeclampsia, and OmicsLonDA identified potential lipid markers that are temporally significantly different between the two groups.Availability and implementationWe provide an open-source R package (https://bioconductor.org/packages/OmicsLonDA), to enable widespread use.Supplementary information Supplementary data are available at Bioinformatics online.

A Novel Space-Borne High-Resolution SAR System with the Non-Uniform Hybrid Sampling Technology for Space Targets Imaging

In order to reduce the complexity of the receiving system for wideband signals, a novel space-borne high-resolution synthetic aperture radar (SAR) system with the non-uniform hybrid sampling technology is proposed in this paper. The non-uniform hybrid sampling technology is firstly applied in the SAR imaging system for the detection of space targets. The non-uniform hybrid sampling technology is able to optimize the transmitted and receiving timing of SAR signals, reducing the requirement of the sampling rate of the analog-to-digital converter (ADC) for the reception of the wideband echoes from space targets. Meanwhile, according to the oversampling requirement of SAR imaging in the azimuth direction, a theoretical model of non-uniform hybrid sampling parameters and relative velocity between the SAR system and the space targets is established. A series of simulation experiments with different targets and different non-uniform hybrid parameters are performed, and an X-band SAR imaging experimental system is constructed to verify the effectiveness of the proposed non-uniform hybrid sampling technology. The experimental results show that the imaging resolution is better than 8 cm. When the non-uniform hybrid sampling interval is 15 us, the imaging quality is consistent with imaging results of the Nyquist real-time sampling, and it is easier to implement in the high-resolution imaging for space targets.

State observer with Round-Robin aperiodic sampled measurements with jitter

A sampled-data observer is proposed for linear continuous-time systems whose outputs are sequentially sampled via non-uniform sampling intervals repeating a prescribed Round-Robin sequence. With constant sampling intervals (jitter-free case) we provide constructive necessary and sufficient conditions for the design of an asymptotic continuous–discrete observer whose estimation error is input-to-state stable (ISS) from process disturbances and measurement noise. We use a time-varying gain depending on the elapsed time since the last measurement. With non-constant sampling intervals (jitter-tolerant case), our design conditions are only sufficient. A suspension system example shows the effectiveness of the proposed approach.

Multi‐rate sampled‐data control of switched affine systems

This study considers the practical stabilisation of switched affine systems under the multi-rate sampled-data switching control. In order to depict the sampled value of all state components, a sensing block composed of several sensors with asynchronous uncertain non-uniform sampling intervals is applied. On the basis of the sampled-data value, a new class of functionals is developed, which is composed of a Lyapunov–Krasovskii functional and a looped function. Practical stabilisation conditions are presented for the switched affine system by means of a switching law. Two examples are provided to demonstrate the effectiveness and feasibility of the proposed results.

Towards Insulin Monitoring: Infrequent Kalman Filter Estimates for Diabetes Management

We propose a Kalman filter-based observer utilizing noisy remote compartment insulin measurements to estimate plasma insulin concentration. The design considers plant-model mismatch, sensor noise, as well as both uniform sampling intervals, mimicking infrequent continuous measurements, and non-uniform sampling intervals, mimicking infrequent on-demand measurements. The performance of the observer is demonstrated on ten in-silico subjects from the UVA/Padova simulator using real-life scenarios, including variability in sensor noise and variability in insulin pharmacokinetics. The proposed observer provides insight into the future use of insulin measurements for diabetes management.

Filtering of T–S Fuzzy Systems With Nonuniform Sampling

The problem of asynchronous filtering of nonlinear systems is investigated in this paper. To facilitate analysis, a discrete-time Takagi-Sugeno fuzzy model with a fast and uniform period is introduced to approximate continuous nonlinear systems. A slow and nonuniform sampler between system and filter is proposed to overcome the contradictions between fast sampling period and limited bandwidth. The nonuniform sampling interval of sampler is subject to a Markov chain. To make full use of the partial information of sampling interval which is accessible to the filter, the asynchronous filter which is described by the hidden Markov model is introduced to reduce conservatism. By resorting to the augmentation approach and the Lyapunov functional method which depends on nonuniform sampling interval, some sufficient conditions for the existence of asynchronous filer are given to guarantee the stability and dissipativity of the augmented system. The gains of asynchronous filter are given via solving a set of linear matrix inequalities. Two examples are utilized to illustrate the validity of the developed filter design technique where the relationships between optimal dissipative performance indices and the mode synchronization rate are given.

On detection of periodicity in C-reactive protein (CRP) levels

C-reactive protein (CRP) is an acute-phase plasma protein that can be used as a biomarker for activation of the immune system. A spectral analysis of CRP level over time for patients with gynaecological tumours has been reported by Madondo et al., using a periodogram method, suggesting that there is no significant periodicity in the data. In our study, we investigate the impact of low sample number on periodogram analysis, for non-uniform sampling intervals—we conclude that data of Madondo et al. cannot rule out periodic behaviour. The search for patterns (periodic or otherwise) in the CRP time-series is of interest for providing a cue for the optimal times at which cancer therapies are best administered. In this paper we show (i) there is no evidence to rule out periodicity in CRP levels, and (ii) we provide a prescription for the minimum data sample rate required in future experiments for improved testing of a periodic CRP signal hypothesis. The analysis we provide may be used for establishing periodicity in any short time-series signal that is observed without a priori information.

Economic design under gamma shock model of the control chart for sustainable operations

The non-uniform sampling scheme and economic statistical design approaches have been successfully applied to determine three parameters of x-bar control charts to monitor a manufacturing process with increasing hazard functions for the last three decades. Nevertheless, a primary assumption for these cost models is that measurements within a sample are independent. However, the conventional supposition may significantly underestimate the type I error probability for the x-bar control chart. Hence, we develop a cost model that combines different researches with the multivariate normal distribution model that given the maximum probability of type I error and the minimum value of power. The optimal parameters of non-uniform sampling interval x-bar control charts are used for the measurements within a sample being correlated. In addition, an industrial example is applied to indicate the solution procedure. Sensitivity analysis is accompanied with input parameters including correlated coefficients as well as process and cost parameters of the model are performed. The genetic algorithm is adopted to reveal the optimal solution of the economic design. The method proposed can be used on related industries to achieve the ability of production monitoring and cost reducing. The human resource consuming and the amount of scraps will be avoided toward the conclusive goals of economic benefit, environmental benefit and social benefit.

Economic statistical design of -control charts: Modified version of Rahim and Banerjee (1993) model

ABSTRACTRahim and Banerjee considered a constant integral of the hazard function for all sampling intervals. This led the sampling intervals to depend on the extended first sampling interval (h1). Since this limitation might not lead to an optimal situation, we first showed that elimination of the mentioned restriction did not cause any significant change in the average quality cycle cost. So if one is looking for an ideal cost and the simplicity of the process, the approach taken in Rahim and Banerjee’s study is the best procedure to adopt. Moreover, in many cases of non-uniform sampling method the first sampling interval becomes so large and this can sometimes lead the production system to the out-of-control state due to unexpected failures that might happen during that time. Therefore, we proposed a new model of uniform and non-uniform sampling intervals combination that allows us to confine the value of h1 without undergoing high costs. The proposed model showed that the quality cycle cost of the proposed model is lower than Rahim and Banerjee’s model in the economic-statistical state. For more illustration, we conducted sensitivity analysis and gave numerical examples.

Observer-based output feedback control of networked control systems with non-uniform sampling and time-varying delay

ABSTRACTThis paper investigates the problem of observer-based output feedback control for networked control systems with non-uniform sampling and time-varying transmission delay. The sampling intervals are assumed to vary within a given interval. The transmission delay belongs to a known interval. A discrete-time model is first established, which contains time-varying delay and norm-bounded uncertainties coming from non-uniform sampling intervals. It is then converted to an interconnection of two subsystems in which the forward channel is delay-free. The scaled small gain theorem is used to derive the stability condition for the closed-loop system. Moreover, the observer-based output feedback controller design method is proposed by utilising a modified cone complementary linearisation algorithm. Finally, numerical examples illustrate the validity and superiority of the proposed method.

Waveform timing performance of a 5 GS/s fast pulse sampling module with DRS4**Supported by Knowledge Innovation Program of the Chinese Academy of Sciences (KJCX2-YW-N27), and National Natural Science Foundation of China (11175176)

We first clarify timing issues of non-uniform sampling intervals regarding a 5 GS/s fast pulse sampling module with DRS4. A calibration strategy is proposed, and as a result, the waveform timing performance is improved to below 10 ps RMS. We then further evaluate waveform-timing performance of the module by comparing with a 10 GS/s oscilloscope in a setup with plastic scintillators and fast PMTs. Different waveform timing algorithms are employed for analysis, and the module shows comparable timing performance with that of the oscilloscope.

A new time calibration method for switched-capacitor-array-based waveform samplers

We have developed a new time calibration method for the DRS4 waveform sampler that enables us to precisely measure the non-uniform sampling interval inherent in the switched-capacitor cells of the DRS4. The method uses the proportionality between the differential amplitude and sampling interval of adjacent switched-capacitor cells responding to a sawtooth-shape pulse. In the experiment, a sawtooth-shape pulse with a 40ns period generated by a Tektronix AWG7102 is fed to a DRS4 evaluation board for calibrating the sampling intervals of all 1024 cells individually. The electronic time resolution of the DRS4 evaluation board with the new time calibration is measured to be ~2.4ps RMS by using two simultaneous Gaussian pulses with 2.35ns full-width at half-maximum and applying a Gaussian fit. The time resolution dependencies on the time difference with the new time calibration are measured and compared to results obtained by another method. The new method could be applicable for other switched-capacitor-array technology-based waveform samplers for precise time calibration.

A Wide Measurement Range and Fast Update Rate Integrated Interface for Capacitive Sensors Array

A CMOS Capacitance-to-Digital Converter (CDC) for capacitive sensors array applications is presented. It consists of a 16:1 multiplexer, a capacitance-to-voltage front-end and a 16-bit voltage-to-pulses converter. The proposed capacitance-to-voltage front-end circuit extends the dynamic range by charging or discharging the measured capacitive sensors indirectly. For low power consumption and short conversion time, hardware reuse technique and multi-steps quantization method have been applied in voltage-to-digital pulse converter design. This 16-ch CDC's maximum absolute input capacitance is 350 pF under a non-uniform distributed sampling interval of 0.15-0.75 ms with 90 μA current consumption under ±0.9 V voltage supply. This prototype chip has been designed and fabricated in 0.18- μm 1P6M CMOS process with active area of 640 × 630 μm2.

Increasing sensitivity in the measurement of heart rate variability: The method of non-stationary RR time–frequency analysis

A novel method of the time–frequency analysis of non-stationary heart rate variability (HRV) is developed which introduces the fragmentary spectrum as a measure that brings together the frequency content, timing and duration of HRV segments. The fragmentary spectrum is calculated by the similar basis function algorithm. This numerical tool of the time to frequency and frequency to time Fourier transformations accepts both uniform and non-uniform sampling intervals, and is applicable to signal segments of arbitrary length. Once the fragmentary spectrum is calculated, the inverse transform recovers the original signal and reveals accuracy of spectral estimates. Numerical experiments show that discontinuities at the boundaries of the succession of inter-beat intervals can cause unacceptable distortions of the spectral estimates. We have developed a measure that we call the “RR deltagram” as a form of the HRV data that minimises spectral errors. The analysis of the experimental HRV data from real-life and controlled breathing conditions suggests transient oscillatory components as functionally meaningful elements of highly complex and irregular patterns of HRV.

BATS: a Bayesian user-friendly software for Analyzing Time Series microarray experiments

BackgroundGene expression levels in a given cell can be influenced by different factors, namely pharmacological or medical treatments. The response to a given stimulus is usually different for different genes and may depend on time. One of the goals of modern molecular biology is the high-throughput identification of genes associated with a particular treatment or a biological process of interest. From methodological and computational point of view, analyzing high-dimensional time course microarray data requires very specific set of tools which are usually not included in standard software packages. Recently, the authors of this paper developed a fully Bayesian approach which allows one to identify differentially expressed genes in a 'one-sample' time-course microarray experiment, to rank them and to estimate their expression profiles. The method is based on explicit expressions for calculations and, hence, very computationally efficient.ResultsThe software package BATS (Bayesian Analysis of Time Series) presented here implements the methodology described above. It allows an user to automatically identify and rank differentially expressed genes and to estimate their expression profiles when at least 5–6 time points are available. The package has a user-friendly interface. BATS successfully manages various technical difficulties which arise in time-course microarray experiments, such as a small number of observations, non-uniform sampling intervals and replicated or missing data.ConclusionBATS is a free user-friendly software for the analysis of both simulated and real microarray time course experiments. The software, the user manual and a brief illustrative example are freely available online at the BATS website:

Bayesian models for two-sample time-course microarray experiments

A truly functional Bayesian method for detecting temporally differentially expressed genes between two experimental conditions is presented. The method distinguishes between two biologically different set ups, one in which the two samples are interchangeable, and one in which the second sample is a modification of the first, i.e. the two samples are non-interchangeable. This distinction leads to two different Bayesian models, which allow more flexibility in modeling gene expression profiles. The method allows one to identify differentially expressed genes, to rank them and to estimate their expression profiles. The proposed procedure successfully deals with various technical difficulties which arise in microarray time-course experiments, such as small number of observations, non-uniform sampling intervals and presence of missing data or repeated measurements. The procedure allows one to account for various types of error, thus offering a good compromise between nonparametric and normality assumption based techniques. In addition, all evaluations are carried out using analytic expressions, hence the entire procedure requires very little computational effort. The performance of the procedure is studied using simulated and real data.

A Bayesian Approach to Estimation and Testing in Time-course Microarray Experiments

The objective of the present paper is to develop a truly functional Bayesian method specifically designed for time series microarray data. The method allows one to identify differentially expressed genes in a time-course microarray experiment, to rank them and to estimate their expression profiles. Each gene expression profile is modeled as an expansion over some orthonormal basis, where the coefficients and the number of basis functions are estimated from the data. The proposed procedure deals successfully with various technical difficulties that arise in typical microarray experiments such as a small number of observations, non-uniform sampling intervals and missing or replicated data. The procedure allows one to account for various types of errors and offers a good compromise between nonparametric techniques and techniques based on normality assumptions. In addition, all evaluations are performed using analytic expressions, so the entire procedure requires very small computational effort. The procedure is studied using both simulated and real data, and is compared with competitive recent approaches. Finally, the procedure is applied to a case study of a human breast cancer cell line stimulated with estrogen. We succeeded in finding new significant genes that were not marked in an earlier work on the same dataset.

A review on Fourier spectrum of D/A outputs with non-uniformly sampled data and time-varying clocks

In this paper, we investigate problems of D/A converters with non-uniformly sampled input data, and/or time-varying clock sources. The input digital data (which are stored in the memory to be read out and sent to a D/A converter) were obtained by sampling an analog waveform at non-uniform sampling intervals. (Quantization of data can also be considered as a form of non-uniform sampling.) Recently, there is available a new clocking system with a very fine time resolution and is capable of adjusting the clock period in a sample-to-sample basis. With so many advances on the technology, there is a need to provide a unified theoretical model for this class of problems. In this paper, we consider the following five different models: f 1( t)=∑ n x( nT) g( t− nT), f 2( t)=∑ n x( t n ) g( t− nT), f 3( t)=∑ n x( nT) g( t− t n ), f 4( t)=∑ n x( t n ) g( t− t n ), and f 5( t)=∑ n x( t n ) g n ( t− t n ) where x(·) is the input analog signal, g(·) is the basic output pulse waveform of the D/A converter, T is the nominal sampling period and t n is the nth sampling time instance (for uniform sampling t n = nT). The first four models have been studied before [IEEE Transactions on Instrumentation & Measurements 45 (1996) 56, IEEE Transactions on Instrumentation & Measurements 46 (1997) 653] and the results are included here for completeness. The result for the fifth model is new. Closed form expressions for the Fourier transform of the output signals for each model are derived.