Discrete measurements

The measurements are put together of discrete measured points. Then the superposition integral valid for continuous signals changes into a superposition addition for discrete signals ... 

Dlsci ete mea.sui ements. An example of a discrete measurement is a level switch that indicates the presence or absence of hquid at the location at which the level switch is installed. 

In continuous processes, most process control applications rely on continuous measurements. In batch processes, many of the process control applications will utihze discrete as well as continuous measurements. In both types of processes, the safety interlocks and process interlocks rely largely on discrete measurements. 

Continuous Measurements In most apphcations, continuous measurements are considerably more ambitious than discrete measurements. Basically, discrete measurements involve a yes/no decision, whereas continuous measurements may entail considerable signal processing. 

Amplitude can be measured as the sum of all the forces causing vibrations within a piece of machinery (broadband), as discrete measurements for the individual forces (component), or for individual user-selected forces (narrowband). Broadband, component, and narrowband are discussed in Section 43.8 Measurement classifications. Also discussed in this section are the common curve elements peak-to-peak, zero-to-peak, and root-mean-square. 

In both of these equations, we have used a summation rather than an integral over the potential energy for both clarity and the connection with the actual, discretized measurements in a simulation. 

The bottom line is that the underlying reason for the problem we ran into is the fundamental difference between a continuous (the Normal case) and a discrete (Poisson) distribution. In the first case, values of exactly zero will never be obtained, although a value may come arbitrarily close to zero and the difference from zero may be unmeasurable by a particular instrument, although we can argue that even in this case the measurement of an exact zero value is an artifact of the discrete measurement levels... 

Finally the formula for n (the number of discrete measurements required) for a given uncertainty as equation 73-6. 

The response to a pulse input of tracer may be monitored continuously or by discrete measurements in which samples are analyzed at successive intervals. If discrete measurements are used, nt0/q0 in equation 19.3-2 is approximated by... 

Consider a solid feed consisting of a mixture of different-size particles. The size distribution of this feed can be represented either as a continuous distribution or as a discrete distribution. We use the latter representation because screen analysis, our way of measuring size distributions, gives discrete measurements. 

The loadings plot is also examined for inherent dimensionality and unusual variables. No conclusions can be drawn because of the limited utility of this diagnostic when examining data sets comprised of discrete measurement variables. 

The POT is a discrete measurement technique using pin type ionization probes as sensors for detecting the arrival time of detonation wave at pre-determined points and measuring propagation time between these points with the help of a high-speed oscilloscope. The schematic of instrumentation set-up is shown in Figure 3.17. 

The advantages of the bipolar pulse technique include speed (discrete measurements at a rate as high as 30 kHz), accuracy, and signal-to-noise ratio. The system has been employed as a detector in automated conductometric titrations and in stopped-flow mixing systems with excellent results. 

Sensing by Continuous Measurement Discrete Measurement Suitable for Comments... 

The data obtained from studies 34 36,54,S5) carried out at fixed y and various T (as in Figs. 5 and 61 show that the time dependence of rieff may be approximated by a linear law. The influence of medium deformation on gelatination can not be determined within the limits of experimental uncertainty. This may be seen, for instance, from Fig. 6a where the dependence t eff(T) at 53 °C was obtained for both the discrete (points 1) and continuous deforming modes (points 2). Figure 6 presents only those Tleff which correspond to the moments of discrete measurements. 

The precision of an analysis is most conveniently defined in terms of percent relative standard deviation. The standard deviation is relatively easily calculated following a series of discrete measurements either of absorbance or of concentration. The relative standard deviation is then defined as the standard deviation expressed as a percentage of the mean of the data used to calculate the standard deviation. 

Figure 5b. Nitrate concentration (gM) data compiled from transects across warm core Ring 81 G. The data are from continuous analysis of pumped water with an autoanalyzer and from discrete measurements of bottle samples during CTD casts. Note the different shape of nitrate-rich intrusions.

Chung, Y., 1985. Radon variations at Arrowhead and Murrieta Springs continuous and discrete measurements. Pure Appl. Geophys., 122 294-358. 

Hernandez, H. and J. Alvarez, 2003, Robust estimation of continuous nonlinear plants with discrete measurements, J. of Process Control, 13, 1, 69-89. 

Not all analytical data can be recorded on a continuous basis discrete measurements often have to be made and they may not be at regular time or space intervals. To predict intermediate values for a smooth graphic di lay, or to perform many mathematical manipulations, e.g. Savitzky-Golay smoothing, it is necessary to evaluate regularly spaced intermediate values. Such values are obtained by interpolation. 

Many analytical measures cannot be represented as a time-series in the form of a spectrum, but are comprised of discrete measurements, e.g. compositional or trace analysis. Data reduction can still play an important role in such cases. The interpretation of many multivariate problems can be simplified by considering not only the original variables but also linear combinations of them. That is, a new set of variables can be constructed each of which contains a sum of the original variables each suitably weighted. These linear combinations can be derived on an ad hoc basis or more formally using established mathematical techniques. Whatever the method used, however, the aim is to reduce the number of variables considered in subsequent analysis and obtain an improved representation of the original data. The number of variables measured is not reduced. 

Far fewer PK/PD analyses and reports deal with PD measures that are discrete in nature. Variables that represent discrete measures have properties that are distinct from continuous variables. A variable is discrete if the number of values that it can assume is finite or countably infinite. Count data is generally considered a type of discrete variable. 

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