Modelling errors with respect to choice of

The integral squared error between the unit impulse response of the process and that of the Nth Laguerre model is defined as 

Using the orthonormal properties of the Laguerre functions, Equation (2.30) is equivalent to 

Equation (2.32) corresponds to the original definition of the Laguerre coefficients in Equations (2.6). It can be shown that the solutions of the coefiicients given by Equation (2.32) minimize the integral squared error in 

Equation (2.29) because the second derivative of E with respect to Cj is always positive. 

Using Parseval s theorem, Equation (2.29) can be also represented in the frequency domain as 

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