First-order filter

Now, our previous result shows that F0(f), being the result of passing X(t) through the linear, time-invariant filter h0(t )> must have a gaussian first-order distribution therefore,... 

M. Gui and S.C. Rutan, Determination of initial concentration of analyte by kinetic detection of the intermediate product in consecutive first-order reactions using an extended Kalman filter. Anal. Chim. Acta, 66 (1994) 1513-1519. 

The literature refers the term as a first order filter. It only makes sense if you recall your linear circuit analysis or if you wait until the chapter on frequency response analysis. 

Gratings also diffract light in the second, third and higher orders. If a grating reinforces light at 600 nm in the first order, it will also reinforce fight at 300 nm in the second order and 200 nm in the third order. Gratings are usually paired with simple optical filters to remove unwanted... 

Example 18.11. Suppose we want to find a discrete approximation for a first-order lag. This would be called a first-order digital filter. Let x, be the output of the filter and m ) be the input. 

Rearranging gives the computer algorithm for a first-order filter using the rectangular integration approximation. 

This is the transfer function for a first-order digital filter. Thus the precompensator slows down the input to the controller so that it does not see a step change in the error signal (see (Fig. 20.3h). 

FIGURE 12-IS Annual growth of the terminal shoot (upper) and first-order branches (lower) in upper half of ponderosa pine saplings maintained in filtered or unfiltered (ambient) air greenhouses, and an outside ambient-air treatment from 1%8 through 1973. Reprinted with permission from Kickert et al. 

Dlchlorophenol in aqueous solution was illuminated with filtered xenon light (A >295 nm) at various time intervals. The first-order conversion rate constant was 5.73 x lO Vsec. The loss of chlorine atoms seemed to be the major early process during the reaction (Svenson and Kaj, 1989). 

A methanogenic consortium derived from municipal anaerobic digester sludge was placed into a reactor containing 1,1,1-trichloroethane. The reactor was operated at 20 °C on an average 50-d hydraulic retention time. Degradation followed first-order kinetics and reported rate coefficients for filtered and unfiltered supernatant from the settled consortium were 0.11 and 0.12/day, respectively. 1,1-Dichloroethane was the only product detected which accounted for 46% of the initial 1,1,1-trichloroethane concentration (Gander et al, 2002). 

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