Dispersion Impulse signal

For the unitary impulse signal (relation (3.100)) the axial dispersion flow model has an analytical solution ... 

The values of the dispersion coefficients will be established for most actual cases by experiments, which pursue the registration and interpretation of the exit time distribution of a signal that passes through a physical reduced model of the real device. However, in some cases, the actual device can be used. The method for identifying the dispersion coefficient [3.27, 3.28] is, in fact, the classical method of flow identification based on the introduction in the device input of a signal (frequently as a 5 impulsion or a unitary impulsion) the exit response is then recorded from its start until it disappears. It is evident that this experimental part of the method has to be completed by calculation of the dispersion model flow and by identification of the value of the dispersion coefficient. For this last objective, the sum of the square differences between the measured and computed values of the exit signal, are minimized. 

Figure 2.11. The impulse response and the step response obtained in a single-line FIA system by injecting a dye solution of concentration C into an inert colorless carrier stream, the signal being recorded as absorbance A. 5 is the point of injection and 5i/2(ti/2) is sample volume (time) necessary to inject sample volume to reach = 2. Vr is the reactor volume, T is the residence time, and D is the dispersion coefficient. [608].

In the previous section, we established a correspondence between the transient time-domain response (exponentially damped cosine wave) to a sudden "impulse" excitation and the steady-state frequency-domain response (Lorentzian absorption and dispersion spectra) to a continuous excitation. The Fourier transform may be thought of as the mathematical recipe for going from the time-domain to the frequency-domain. In this section, we shall introduce the mathematical forms of the transforms, along with pictorial examples of several of the most important signal shapes. 

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