Discrete data sampling

The strategy depends on the situation and how we measure the concentration. If we can rely on pH or absorbance (UV, visible, or Infrared spectrometer), the sensor response time can be reasonably fast, and we can make our decision based on the actual process dynamics. Most likely we would be thinking along the lines of PI or PID controllers. If we can only use gas chromatography (GC) or other slow analytical methods to measure concentration, we must consider discrete data sampling control. Indeed, prevalent time delay makes chemical process control unique and, in a sense, more difficult than many mechanical or electrical systems. 

Discrete Data. The underway data were calibrated with discrete samples drawn from the flow about every 15 min. On occasion, especially in sharp frontal regions, calibration samples were drawn more frequently. A detailed description of each calibration procedure is given here. 

With the present lack of synoptic tools for surveying bacterial abundance, data on the abundance and production of heterotrophic bacteria in the Eastern Mediterranean are more sporadic than for phytoplankton chlorophyll and depend on discrete depth sampling and analysis. The data available are for the Cyprus Eddy in summer (Zohary Robarts, 1992) and in winter (Zohary etal., 1998), and in the Cretan Sea in March and September (van Wambeke etal., 2000), and a general survey of the Levantine Basin in fall (Robarts etal., 1996). Some additional data exists for the Western Mediterranean which will not be reviewed here. 

Chapters 27,28,29. The material in these chapters has by now become classic and the reader can consult several good references for more details. The following two texts provide an excellent treatment on the mathematical analysis of discrete-time (sampled-data) systems ... 

This section considers the response measurement of a single-degree-of-freedom system or a single-channel measurement of a multi-degree-of-freedom system. Discrete data is sampled with a time step Ar and y denotes the measured response at time t = nAt. The measurement is different from the model response ... 

Discrete data are sampled with a time step At and y are then used to denote the measured response at time t = nAt. Due to measurement noise and modeling error, there is a difference between the measured response y and the model response x nAt), referred to hereafter as prediction error. It is assumed that the prediction error can be adequately represented by a... 

Whenever the same parameters are available from two different curves (e.g., wq aiid t from Figure 1 or Figure 4a), there is some mathematical relation between the curves. For the "linear" system we have considered (i.e., displacement is proportional to driving amplitude Fq) the time-domain and frequency-domain responses are connected by a Fourier transform. Similarly, absorption and dispersion spectra both yield the same information, and are related by a Hilbert transform (see Chapter 4). In this Chapter, we will next develop some simple Fourier transform properties for continuous curves such as Figures 1-4, and then show the advantages of applying similar relations to discrete data sets consisting of actual physical responses sampled at equally-spaced intervals. 

Create the functional sample. The curves are created based on discrete data, recording each function based on an expansion of basic functions [7]. In this way, there is a functional sample, where each function represents the measurement already within a complete time unit. 

Quantile n An element in the set of location values that divide the set of observations, data sample, population, or probability distribution into groups containing equal numbers of observations. In the case of discrete sets, equal means as equal as possible. There are several common types of quantiles based on the number of groups quartile = four groups, quintile = five groups, decile = ten groups, percentile or centile = one hundred groups. 

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