In this paper, we continue a topic of modeling measuring processes by perceiving them as a kind of signal sampling. And, in this respect, note that an ideal model was developed in a previous work. Whereas here, we present its nonideal version. This extended model takes into account an effect, which is called averaging of a measured signal. And, we show here that it is similar to smearing of signal samples arising in nonideal signal sampling. Furthermore, we demonstrate in this paper that signal averaging and signal smearing mean principally the same, under the conditions given. So, they can be modeled in the same way. A thorough analysis of errors related to the signal averaging in a measuring process is given and illustrated with equivalent schemes of the relationships derived. Furthermore, the results obtained are compared with the corresponding ones that were achieved analyzing amplitude quantization effects of sampled signals used in digital techniques. Also, we show here that modeling of errors related to signal averaging through the so-called quantization noise, assumed to be a uniform distributed random signal, is rather a bad choice. In this paper, an upper bound for the above error is derived. Moreover, conditions for occurrence of hidden aliasing effects in a measured signal are given.

To stabilise the periodic operation of a chemical reactor the oscillation period should be determined precisely in real time. The method discussed in the paper is based on adaptive sampling of the state variable with the use of chaotic mapping to itself. It enables precise determination of the oscillation period in real time and could be used for a proper control system, that can successfully control the process of chemical reaction and maintain the oscillation period at a set level. The method was applied to a tank reactor and tubular reactor with recycle.

In a parallel time-interleaved data sampling system, timing and amplitude mismatches of this structure degrade the performance of the whole ADC system. In this paper, an adaptive blind synthesis calibration algorithm is proposed, which could estimate the timing, gain and offset errors simultaneously, and calibrate automatically. With no need of an extra calibration signal and redesign, it could efficiently and dynamically track the changes of mismatches due to aging or temperature variation. A fractional delay filter is developed to adjust the timing mismatch, which simplifies the design and decreases the cost. Computer simulations are also included to demonstrate the effectiveness of the proposed method.

The paper presents an impedance measurement method using a particular sampling method which is an alternative to DFT calculation. The method uses a sine excitation signal and sampling response signals proportional to current flowing through and voltage across the measured impedance. The object impedance is calculated without using Fourier transform. The method was first evaluated in MATLAB by means of simulation. The method was then practically verified in a constructed simple impedance measurement instrument based on a PSoC (Programmable System on Chip). The obtained calculation simplification recommends the method for implementation in simple portable impedance analyzers destined for operation in the field or embedding in sensors.

In this paper, we present some useful results related with the sampling theorem and the reconstruction formula. The first of them regards a relation existing between bandwidths of interpolating functions different from a perfectreconstruction one and the bandwidth of the latter. Furthermore, we prove here that two non-identical interpolating functions can have the same bandwidths if and only if their (same) bandwidth is a multiple of the bandwidth of an original unsampled signal. The next result shows that sets of sampling points of two nonidentical (but not necessarily interpolating) functions possessing different bandwidths are unique for all sampling periods smaller or equal to a given period (calculated in a theorem provided). These results are completed by the following one: in case of two different signals possessing the same bandwidth but different spectra shapes, their sets of sampling points must differ from each other.

We present here a few thoughts regarding topological aspects of transferring a signal of a continuous time into its discrete counterpart and recovering an analog signal from its discrete-time equivalent. In our view, the observations presented here highlight the essence of the above transformations. Moreover, they enable deeper understanding of the reconstruction formula and of the sampling theorem. We also interpret here these two borderline cases that are associated with a time quantization step going to zero, on the one hand, and approaching its greatest value provided by the sampling theorem, on the other

In this paper, we show that signal sampling operation can be considered as a kind of all-pass filtering in the time domain, when the Nyquist frequency is larger or equal to the maximal frequency in the spectrum of a signal sampled. We demonstrate that this seemingly obvious observation has wideranging implications. They are discussed here in detail. Furthermore, we discuss also signal shaping effects that occur in the case of signal under-sampling. That is, when the Nyquist frequency is smaller than the maximal frequency in the spectrum of a signal sampled. Further, we explain the mechanism of a specific signal distortion that arises under these circumstances. We call it the signal shaping, not the signal aliasing, because of many reasons discussed throughout this paper. Mainly however because of the fact that the operation behind it, called also the signal shaping here, is not a filtering in a usual sense. And, it is shown that this kind of shaping depends upon the sampling phase. Furthermore, formulated in other words, this operation can be viewed as a one which shapes the signal and performs the low-pass filtering of it at the same time. Also, an interesting relation connecting the Fourier transform of a signal filtered with the use of an ideal low-pass filter having the cut frequency lying in the region of under-sampling with the Fourier transforms of its two under-sampled versions is derived. This relation is presented in the time domain, too.

Reconciliation between two copper ore mines transferred ore from one mine to another for processing in enrichment plants generated the need to regularly study the amount and composition of the ore on the conveyor connecting these two mines. To ensure the objectivity of the study, taking composite samples and their analysis was entrusted to a specialized outside laboratory. However, the managing staff of both mines still have doubts whether sampling results reflect correctly content of transported ore especially when the fed is highly variable. In order to investigate how the relatively low sampling rate affects the accuracy and precision of the measurement, the article investigates the hypothetical situation on the linking conveyor with the ore having extremely differentiated mineralization: 80% of almost barren rock (below 0.7% Cu) and 20% of the richly mineralized shale (around 10% Cu). Such ore occurs in some areas of the mine, from which it is fed onto a connecting conveyor. Through simulation techniques it was examined how the frequency of sampling can influence the distribution of the pooled sample results. It turned out that for 16 randomly selected samples in the following 15 minutes time intervals of a working shift, the spread of results around the simulated value is very large. A satisfactory accuracy level for the estimations of mean Cu content in the transported ore is achieved when the samples are collected at 30-second intervals. Only with sampling frequency close to on-line scanner parameters the probability of obtaining estimations with deviation exceeding 10% drops to the level of 2%. In the case of extremely differentiated ore doubts about confidence in the described measurements are fully confirmed, because with over 50% probability a single measurement could be deviated by 50% up and down from the true value.

Cephus fumipennis Eversmann is a key insect pest of wheat crops in Qinghai, China. Its field population densities were surveyed by using both the back-loaded insect vacuum and a sweep net. Mean densities in township-level were calculated and a quantitative relation, ŷ = 0.664 + 0214x, was established between the two sampling methods. The empirical relationship may be applicable in density monitoring and Integrated Pest Management program of the insect.

Analyses of the ground waters in respect of presence of residues of plant protection products, i.e. active substances as well as environmental metabolites thereof are performed in the Institute of Plant Protection since the end of 80ties of the past Century. Based on the results obtained in 1993–1994 for 40 wells located in administrative territories of former Poznań, Toruń and Bydgoszcz voivodeships, in the vicinity of intensive agricultural production areas (orchards, farms), wells where significant amounts of residues of triazines group and dealkylated metabolites thereof had been found previously were qualified to further studies. There were 6 wells in which triazine residues were determined most often. Additionally, based on hydrogeological maps, directions of underflows in the areas of well’s locations were determined as well. The aim of the above was to find the additional places for sampling waters distant from pollution sources and estimation of the level of residues of target compounds depending on distance from the basic wells. Seven triazine compounds including basic active substances (atrazine, simazine) and their metabolites [desethyl atrazine, desisopropyl atrazine, desethyldesisopropyl atrazine, hydroxyatrazine and hydroxysimazine] were selected for the presented studies. Residues were analyzed using methodologies designed in the Institute, i.e. solid-phase extraction (SPE) followed by determination by chromatographic techniques HPLC-PDA, GC-NPD and GC-MS. Generally, during 11 years of investigations (1993–2003) samplings were performed 52 times and 323 samples of groundwater including that from additional wells were analyzed. Most often residues of atrazine and deethylatrazine in wells located in environs of Poznań were detected.

With the increasing number of electric vehicles (EVs), the disordered charging of a large number of EVs will have a large influence on the power grid. The problems of charging and discharging optimization management for EVs are studied in this paper. The distribution of characteristic quantities of charging behaviour such as the starting time and charging duration are analysed. The results show that charging distribution is in line with a logarithmic normal distribution. An EV charging behaviour model is established, and error calibration is carried out. The result shows that the error is within its permitted scope. The daily EV charge load is obtained by using the Latin hypercube Monte Carlo statistical method. Genetic particle swarm optimization (PSO) is proposed to optimize the proportion of AC 1, AC 2 and DC charging equipment, and the optimal solution can not only meet the needs of users but also reduce equipment investment and the EV peak valley difference, so the effectiveness of the method is verified.

Over the last decades the method of proper orthogonal decomposition (POD) has been successfully employed for reduced order modelling (ROM) in many applications, including distributed parameter models of chemical reactors. Nevertheless, there are still a number of issues that need further investigation. Among them, the policy of the collection of representative ensemble of experimental or simulation data, being a starting and perhaps most crucial point of the POD-based model reduction procedure. This paper summarises the theoretical background of the POD method and briefly discusses the sampling issue. Next, the reduction procedure is applied to an idealised model of circulating fluidised bed combustor (CFBC). Results obtained confirm that a proper choice of the sampling strategy is essential for the modes convergence however, even low number of observations can be sufficient for the determination of the faithful dynamical ROM.