The major requirements of the PRBN method are that the flat bandwidth of ®m(ra) must exceed that of H(jo) by a significant amount, and that the PRBN repeat time, NAt, must be much longer than the settling time of the impulse response, h(t).

Often when a physiological system is characterized, the interest is in obtaining an accurate black-box model of the system dynamics to use in a model-reference control system, such as the Smith delay compensator (Northrop, 1999). The ability to be able to subdivide the model into subsystems that can be related to the physiological and biochemical components of the system is sacrificed. To design a controller to regulate some variable in the physiological system, the model only needs to be accurate mathematically (constants, natural frequencies, order, etc.). Widrow and Stearns (1985) have described a simple black-box approach in which a discrete finite impulse response (FIR) filter of order N is "tuned" to match the input/output characteristics of an unknown plant (system). The plant is discretized, i.e., its input is discrete (sampled) broadband noise, [xk], and its output [dk] is also sampled at the same rate. The same sampled noise is the input to the adaptive model FIR filter, whose output [yk] is subtracted from the plant's output to generate an error, [ek].

The sequence [ek] is used to calculate the MSE, ek . The least-mean-squared (LME) error method is used to find an optimum set of the j = L + 1 coefficients, [wjk], used in the adaptive linear combiner form of the model system, shown in Figure 8.0-4. That is, the optimum vector, W* = [W0 w*1 W2 ... wL], where the w* are the optimum coefficients produced by the LMS process. The LMS process is too complicated to describe here; the interested reader should consult Widrow and Stearns (1985). These authors give examples of using the LMS modeling approach to characterize physiological systems (but not neural systems).

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