1094-6969/04/$20.00©2004IEEE June 2004 IEEE Instrumentation & Measurement Magazine 43 A digital signal processing (DSP) based stand- alone measurement system is capable of mak- ing decisions in control. The role of DSP in measurement microsystems is in ◗ the methodology of solving a fundamental problem of measurand reconstruction ◗ the underlying problem of calibration of measurement channels. Both problems appear and are solved in any measuring sys- tem; their solution in measurement microsystems is specific only by the way of implementation. They will be formulated and explained in the next section using a model of measure- ment especially designed for this purpose. This article explains the applications of DSP measur- and reconstruction and defines and illustrates three class- es of elementary problems: scalar nonlinear problems of static reconstruction, scalar linear problems of dynamic reconstruction, and scalar nonlinear problems of quasi- dynamic reconstruction. The unique objective of measurement is to provide an esti- mate of a measurand, its approximate value, and uncertainty of its value [1]. The measurand is “the generalized quantity to be measured,” [2]; it may denote a scalar quantity, a vector of quantities to be measured, or their functional relationship. For the sake of simplicity, this term is also applied to mathe- matical models of physical quantities to be measured. Model of Measurement There are various models of measurement that may be found in the relevant literature, each fit to the objectives of the research or engineering activity for which it is designed. A measurement situation is viewed differently by the designer of a measuring system for environmental monitor- ing, by the designer of a particular sensor for this system, and by an engineer who is responsible for DSP in this sys- tem. To correctly support the exchange of information in any part of the system, a corresponding model should creat- ed. The model should emphasize relevant aspects of its function and de-emphasize or ignore others. Using this rea- soning, a model of measurement is shown in Figure 1 that facilitates communication on key issues related to DSP in measuring systems. Let’s start its description with an assumption that all symbols used in this figure may denote scalar variables, vec- tors, matrices, functions, or more complex operators. In par- ticular, a variable X modeling a measurand can represent: ◗ a scalar quantity x, e.g., temperature, pressure, or voltage ◗ a vector quantity x = [x 1 x 2 ...] T ; e.g., a vector of tem- peratures in an interior or a vector of mixed quantities (temperature, pressure and analyte concentrations) characterizing an industrial process; ◗ a scalar or vector function of a scalar variable ( t ) or vector variable (t = [ t 1 t 2 ,...] T ) – x ( t ) , x ( t ) , x (t) or x (t); e.g., an optical spectrum being a function model- ing the dependence of light intensity on wavelength or a vector of functions modeling the dependence of the voltages (in an electronic circuit) on time. A measurement object is characterized by two variables, a measurand X and a generalized influence quantity V . Roman Z. Morawski A look at applications and three elementary problems Digital Signal Processing in Measurement Microsystems