Impulse response curve

In this problem the Gram-Charlier will be compared with the Gamma Gauss distributions for an impulse response curve with the equation... 

For larger extents of dispersion, DjuL > 0.01, the shape of impulse response curves f(0) depends on whether reactor boundaries are assumed open or closed. Equation (72) gives the form of such curves when both boundaries are open and Fig. 17 is a plot of eqn. (72) for specific values... 

Fig. 17. Impulse response curves for specified values of DjuL as predicted by eqn. (72) this applies for large extents of dispersion, DjuL > 0.01.

Figure 3-12 Impulse response curves calculated by F.q (3-60) (after Mtilstiura et of. )...

Impulse Response Curve from a Four-Stage Fermenter... 

The amount of shift needed for each temperature point can be graphed, as shown in Figure 6.15. Thus the time-temperature equivalence can be calibrated for a particular pad and used to identify the probable shift in the impulse response curve that could be expected during a typical CMP process. 

Applying the shift factor plot to the impulse-response curve with typical temperatures generated during the CMP process, a reasonable estimate of the shift can be obtained. An example of such a set of shift curves is shown in Figure 6.16. 

Figure 6.16 An example of shifting the impulse-response curve through temperature effects.

All described sensor probes scan an edge of the same material to get the characteristic step response of each system. The derivation of this curve (see eq.(4) ) causes the impulse responses. The measurement frequency is 100 kHz, the distance between sensor and structure 0. Chapter 4.2.1. and 4.2.2. compare several sensors and measurement methods and show the importance of the impulse response for the comparison. 

The following examples represent the importance of the impulse response for the comparison of different magnetic field sensors. For presentation in this paper only one data curve per method is selected and compared. The determined signals and the path x are related in the same way like in the previous chapter. 

This is visible in the behaviour of the impulse responses as well (fig, 7), There the amplitude of curve (1) (gWng, )) is the highest, of curve (2) ig(L,)) the lowest, but the maxima are not located at the same place. 

The difference in widths of the impulse responses are small. Especially visible the pulse response of the inductive sensors, curves (1) and... 

Effluent response curves for perfect impulse injection of tracer (axial dispersion model). (Adapted from Chemical Reaction Engineering, Second Edition, by O. Levenspiel. Copyright 1972. Reprinted by permission of John Wiley and Sons, Inc.)... 

The same solution presented in Fig. 14 can easily be recast (see Ref. 22) into another form, as in Fig. 15. Note here that the maximum scaled response curve is now essentially a rectangular hyperbola with one asymptote which depends only on the level of applied peak force and another asymptote which depends only on the level of applied total impulse. In the intermediate loading regime (the "knee" of the hyperbola), response determination requires knowledge of both peak force and total impulse. 

A test with an impulse input of tracer gave a parabolic response curve... 

The response curve to an impulse input of tracer is a triangle with the equations... 

The response curve of an impulse input has the shape of a trapezoid with equations,... 

The response curve of impulse input to a reactor is semicircular with equation... 

The tracer response curve of impulse input to a reactor is a trapezoid with the given equations. For a second order reaction with kC0 = 2, find the... 

A reactor has a tracer response curve from an impulse input with the equation C = 0.5 cos(-nt/4) over the range 0 t 2. A reaction A= B=>C with k2 =... 

Fortunately, it is not always necessary to recover the system RTD curve from the impulse response, so the complications alluded to above are often of theoretical rather than practical concern. In addition, the dispersion model is most appropriately used to describe small extents of dispersion, i.e. minor deviations from plug flow. In this case, particularly if the inlet pipe is of small diameter compared with the reactor itself, the vessel can be satisfactorily assumed to possess closed boundaries [62]. An impulse of tracer will enter the system and broaden as it passes along the reactor so that the observed response at the outlet will be an RTD and will be a symmetrical pulse, the width of which is a function of DjuL alone. 

Data are often normalized so that the area under the curve is preserved. This area is given by the dc spectral term, that is, for /t = 0. To preserve the area in the discrete inverse-filtered result, every term should be multiplied by the dc spectral components of the impulse response function (if the impulse response function has not been normalized earlier). We would then have ford... 

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