Approximation of the process transfer function

In parallel with the above time domain description, an approximation of the process transfer function using the Laguerre functions can also be developed. The Laplace transform of the impulse response h t) in Equation (2.5) leads to the continuous-time transfer function of the process 

The process transfer function given by Equations (2.9) and (2.10) is called the Laguerre model. The Laguerre filters in Equation (2.10) have a simple 

Condition (2.7), that permitted the use of a truncated expansion to closely approximate the unit impulse response h t), may also be given in the frequency domain by direct application of Parseval s theorem as 

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