Non-uniform Sampling Intervals Research Articles

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.

Nonuniform Sampling for Detection of Abrupt Changes

In this work, detection of abrupt changes in continuous-time linear stochastic systems and selection of the sampling interval to improve the detection performance are considered. Cost functions are proposed to optimize both uniform and nonuniform sampling intervals for the well-known cumulative sum algorithm. Some iterative techniques are presented to make online optimization computationally feasible. It is shown that considerable improvement in the detection performance can be obtained by using nonuniform sampling intervals.

Joint economic design of x and R charts under Weibull shock models

This paper deals with the joint economic design of x and R charts when the occurrence times of assignable causes follow Weibull distributions with increasing failure rates. The variable quality characteristic is assumed to be normally distributed and the process is subject to two independent assignable causes (such as tool wear-out, overheating, or vibration). One cause changes the process mean and the other changes the process variance. However, the occurrence of one kind of assignable cause does not preclude the occurrence of the other. A cost model is developed and a non-uniform sampling interval scheme is adopted. A two-step search procedure is employed to determine the optimum design parameters. Finally, a sensitivity analysis of the model is conducted, and the cost savings associated with the use of non-uniform sampling intervals instead of constant sampling intervals are evaluated.

Economic design of ?? andR charts under Weibull shock models

This paper considers the problem of a continuous production process where both the mean and variance are simultaneously monitored by an X̄ and R chart respectively, and generalizes the model of Costa (IIE Transactions 1993; 25(6):27–33). The product variable quality characteristic is assumed to be normally distributed and the process is subject to two independent assignable causes (such as tool wear-out, overheating or vibration). One cause changes the process mean and the other changes the process variance. However, the occurrence of one kind of assignable cause does not preclude the occurrence of the other. It is also assumed that the occurrence times of the assignable causes are described by Weibull distributions with increasing failure rates. A cost model is developed and a non-uniform sampling interval scheme is adopted. A two-step search procedure is employed to determine the optimal design parameters. The relative contribution of the paper over the results obtained by Costa is addressed. A sensitivity analysis of the model is conducted and the cost savings associated with the use of non-uniform sampling intervals instead of constant sampling intervals are evaluated. The economic design model is then extended to an economic–statistical design model for achieving desired levels of statistical performance while minimizing the expected cost. Performances of purely economic design and economic–statistical design are compared. Copyright © 2000 John Wiley & Sons, Ltd.

Manoeuvre detection for non-uniform sampling intervals

A simple method is presented for determining a detection threshold in a manoeuvre detector in the case of non-uniform sampling intervals. The decision statistic used by the manoeuvre detector is the exponentially-discounted average of the normalised innovations squared.

Optimal nonuniform sampling interval and test-input design for identification of physiological systems from very limited data

Optimal design of test-inputs and sampling intervals in experiments for linear system identification is treated as a nonlinear integer optimization problem. The criterion is a function of the Fisher information matrix, the inverse of which gives a lower bound for the covariance matrix of the parameter estimates. Emphasis is placed on optimum design of nonuniform data sampling intervals when experimental constraints allow only a limited number of discrete-time measurements of the output. A solution algorithm based on a steepest descent strategy is developed and applied to the design of a biologic experiment for estimating the parameters of a model of the dynamics of thyroid hormone metabolism. The effects on parameter accuracy of different model representations are demonstrated numerically, a canonical representation yielding far poorer accuracies than the original process model for nonoptimal sampling schedules, but comparable accuracies when these schedules are optimized. Several objective functions for optimization are compared. The overall results indicate that sampling schedule optimization is a very fruitful approach to maximizing expected parameter estimation accuracies when the sample size is small.