Pulse Function Stimulus-Response Method

The entire amount of the tracer is fed to the reactor inlet within a very short time to approach the Dirac delta function as close as possible. The Dirac function has the following properties  

In practice, the input time should be small compared to the space time 

The experimental C-curve corresponds to the RTD defined in Equation 3.1 for systems closed for dispersion (see Section 3.4.2). In this case C(t) = (t). 

The estimation of mean residence time and variance are illustrated in Example 3.1. The situation is different for systems open for dispersion as discussed in Section 3.4.2. Under these conditions the experimentally determined C-curve is 

The RTD of a tubular reactor is measured with the pulse function stimulus-response method. The experimental results are summarized in Table 3.1  

---

In time domain measurements, the electrochemical system is subjected to a potential variation that is the resultant of many frequencies, like a pulse or white noise signal, and the time-dependent current from the cell is recorded. The stimulus and the response can be converted via Fourier transform methods to spectral representations of amplitude and phase angle frequency, from which the desired impedance can be computed as a function of frequency. 

Not all bioelectric potentials are periodic. In many cases, single pulse signals are observed, such as neural response to a single stimulus. The Fourier-series method of spectral analysis does not apply in such cases as it is defined for periodic functions only. It can be extended, however, through a series of limiting processes to develop the Fourier transform integrals which are defined below. 

---