Search

This paper describes a novel approach to the evaluation of the errors associated with the sampling strategy and the windowing process in digital spectral analysis. The proposed procedure, which is based on the introduction of a general expression for the estimation of input signal spectral components capable of separately pointing out the different sources of error, has been applied to the cascade of any number of rectangular windows in presence of periodic sampling. In addition, the approach has been further developed by assuming that the initial sampling time instant could be randomized, so that each spectral component estimated can be considered as a random variable, described through the classic statistical parameters. These parameters quantify the uncertainty associated with the windowing process considered and the sampling scheme adopted. In this paper, they have been theoretically deduced in a closed form in the case of a cascade of two and three rectangular windows respectively, along with a generalisation to the cascade of any number of elements, and compared with those of the single window in terms of the specific errors due to the sampling and windowing (i.e. resolution, leakage and aliasing). In particular, it has been shown that the cascaded technique can carry out a substantial reduction of the uncertainty associated with the input signal harmonic estimates. The comparison between theoretical findings and simulations is provided, showing a very good agreement.

A nonlinear dynamic "black box" model for sample-hold and analogue to digital conversion devices (S/H-ADCs) is proposed in this paper. It derives from the expansion of a Volterra-like series (previously introduced by authors for the general-purpose modelling of nonlinear dynamic systems) and it is based on a discrete convolution in the time domain, which describes the nonlinear dynamics of the system. The model carries out a functional description of the S/H-ADC nonlinear behaviour as the sum of two blocks which take separately into account the static and the purely dynamic contributions. Model characterization can be performed by means of a simple and reliable measurement procedure and the model analytical representation allows an easy implementation in the framework of commercial available CAD tools for circuit analysis and design. Preliminary experimental results, which validate the proposed approach, are presented in the paper together with some examples which show model capabilities in characterizing the device nonidealities under both DC and large-signal operating conditions.

The empirical “black-box” characterization of non-linear systems with memory is a complex problem which cannot be dealt with by means of a unique, general-purpose mathematical approach such as the Volterra series. In fact, from a metrological point of view, the feasibility and reliability of the measurement procedure must be the criterion on the basis of which any mathematical approach for modelling purposes must be evaluated. This paper describes different solutions for the behavioural identification of non-linear dynamic systems, all based on a modified Volterra series, which are characterized by a reduced number of operators with respect to the classical Volterra approach. The operator reduction, which does not affect the accuracy of the obtained models if a mild assumption on the system memory time duration is satisfied, allows a reliable extraction of the model parameters by means of conventional instrumentation, without the need for the generation of complicated input probing signals or additional approximations. A detailed discussion is provided in order to estimate when each of the proposed approaches can be practically used, by pointing out the hypotheses that must be taken into account in order to minimise the modified series truncation errors. Experimental examples, showing the validity of the proposed approaches, are given in the last section of the paper, as well as a comparison between the performances of the different solutions when applied to the important field of electron device characterization.

A new technique for power spectrum analysis is introduced, theoretically evaluated, and experimentally verified with a prototype. This technique is based on the estimate of the autocorrelation function for different delays. The proposed sampling strategy is random in the time domain and equally spaced, synchronous with the signal, in the delay domain, It is shown that the estimate of the power spectral components is asymptotically unbiased, and the experimental results are also given.

A different procedure for evaluating the errors introduced by the equally-spaced sampling technique in the asynchronous spectral analysis of a periodic signal was introduced. It is based on the assumption that the initial sampling instant can be randomized so that each estimated spectral component can be considered a random variable characterized by its statistical parameters. The theoretical expressions of these parameters were deduced and compared with the simulated ones denoting a very good agreement between them.

A new model has been proposed for the characterisation of the non-linear dynamic effects of a S/H-ADC device and a new mathematical approach has been introduced to describe its non-ideal dynamic behaviour. The measurement procedure to deduce the parameters of the proposed model is given together with the experimental results on a commercial device.

A recursive random-sampling strategy is proposed for the implementation of a digital broadband wattmeter. In this strategy each sampling instant is obtained by adding to the preceding one a predetermined constant lag plus a random increment. In order to correlate the measurement uncertainty to the bandwidth, the asymptotic mean-square error arising from the sampling strategy and the filtering algorithm is evaluated and analyzed; it has been shown that the proposed sampling strategy does not limit the bandwidth of the instrument if an appropriate statistical distribution of the random increments is selected. The theoretical results are compared with those obtained by simulating the measurement process. >

A method for the performance evaluation of digital measurement instruments based on asynchronous sampling and nonlinear signal conversion is proposed. The authors propose a performance index for the comparison of different asynchronous strategies and develop the analytical form of that index for two sampling techniques, equally spaced and random. The idea is to interpret the instantaneous output of the instrument as a discrete random variable with a uniform distribution over the successive occasions of measurement. Thus, the asymptotic variance of the reading can be a sum of contributions, each of which is obtained by weighting the contributions relative to each spectral component of the signal according to a frequency-dependent coefficient which is assumed to the performance index. >

A new interesting technique for fault diagnosis in non-linear analog systems is presented. The approach is based on a neural network interpolator for the construction of a fault dictionary in the frequency domain. A multi-layered architecture with one hidden layer is chosen in order to locate and to identify the most likely faulty element of the System Under Test (SUT). >

This paper presents a digital harmonic vector voltmeter based on a random asynchronous sampling strategy. The measurement procedure is described and the problem of estimating both the error due to the time discretization and to the estimation of the periodic complex exponential associated with the input reference signal is discussed. >

The explicit recognition of uncertainty is central to any measurement process. In this work a computer-intensive approach is adopted to the estimation of uncertainty at a given coverage probability, that is, at a given region of confidence in a measurement process. The method is adaptable to a large range of situations and is based on the use of Monte Carlo approximation and bootstrap resampling iteration. An experimental model is examined to understand the applicability of the numerical technique and to check the potentiality of the proposed method.

This paper describes a power spectrum analyzer whose bandwidth is not limited by the mean sampling time. The procedure is based on the estimation of the spectral components of the autocorrelation function of the input signal through the simultaneous random sampling of the given input signal and its randomly "delayed copy". The samples are therefore randomly taken in a double-dimension space, time, and delay. By using a random process in the time domain with a recursive mean previously introduced by the authors in order to avoid any bandwidth limitation due to the sampling strategy, it is shown both theoretically and through simulation that the estimate of the power spectral components is asymptotically unbiased on the unique hypothesis of a synchronized random sampling in the delay domain, i.e., the sampling delays are uniformly distributed in an interval equal to the period of the input signal. The simulation results confirm the theoretical findings.

In this paper, some recent theoretical developments are reviewed and associated algorithms are proposed to determine the numerical testability for large multiinput multioutput systems. In our approach, the modified nodal analysis and the usual techniques for the sensitivity computation in the frequency domain are employed. According to the theoretical basis provided by Sen and Saeks [1] the testability evaluation is related to the computation of the number of linearly independent columns in a convenient form of the sensitivity matrix with rational entries having a common denominator. Then, by extending some results already obtained in [3], it is shown that the above-mentioned number can be determined by computing the numerical rank of a matrix comprised of the coefficients obtained by expanding the numerators of the sensitivities in a suitable orthogonal polynomial series. The numerical rank computation is simplified, particularly for large systems, through an algorithm based on the estimation of the polynomial degrees, which is performed by the iterative comparison between the Chebycheff and the corresponding Stirling coefficients.

der to obtain a measurement result independent of the meas- urement occasion, the ratio between each spectral component and the fundamental one is introduced. It has been shown that the mean value of this new parameter is independent from the measurement occasion if the number of samples is suffi- ciently large and

This paper describes a spectrum analyzer based on a random asynchronous sampling strategy, previously introduced by the authors, whose bandwidth limitation is due uniquely to the bandwidth of the Sample/Hold circuit. The properties of the proposed estimate of each spectral component based on the discretization of the Fourier series, are deduced by considering the statistical parameters of the output. In order to obtain a result independent from the generic measurement occasion, the asymptotic expected value is deduced; however this last results null. In order to overcome this cumbersome, each estimate of the spectral components is normalized with respect to the fundamental frequency. In the paper it is shown that the mean value of this new parameter is independent from the measurement occasion if the number of samples is sufficiently great; besides it is characterized by a bias which depends on the approximation of the estimated fundamental frequency of the signal with respect to its true value. At last a procedure to estimate the fundamental frequency is proposed.