Some special cases of disturbances

By imposing some assumptions on the power spectrum of the disturbance, we can obtain explicit expressions for the variances of the estimated Laguerre coefficients. 

Assume that t) = D -cos wot -H 9) with its corresponding power spectrum given by (Unbehauen and Rao, 1987) 

Assume that t) is a disturbance with band-limited spectrum satisfying 

Therefore, if the interval [toi, t02] is in a higher frequency region where Wi(to) is small, then the error in the estimated coefficient Cj will be small. 

If t) is a continuous-time white noise sequence with autocorrelation function and power spectrum given by, for all t and all w 

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