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The problem of nonparametric function fitting with the observation model y i = f (x i ) + η i , i = 1, . . . , n, is considered, where η i are independent random variables with zero mean value and finite variance, andform a random sample from a distribution with density ∈ L 1 [a, b] and are independent of the errors η i , i = 1, . . . , n. The asymptotic properties of the estimator f N (n) b] and c N (n) = ( c 1 , . . . , c N (n) ) T obtained by the least squares method as well as the limits in probability of the estimators c k , k = 1, . . . , N , for fixed N , are studied in the case when the functions e k , k = 1, 2, . . . , forming a complete orthonormal system in L 2 [a, b] are analytic.1991 Mathematics Subject Classification: Primary 62G07, 62F12.

In this work theoretical foundations of the Fourier Transform Band Pass Filter (FTBPF) technique are developed which show that such procedure is applicable to extraction of irregular monochromatic oscillations with time-varying amplitudes and phases from the analyzed signal data. Considerations concerning the statistical error of the FTBPF coherence between two filtered oscillations are included. Further certain method of the filter pass-band width parameter determination is proposed and relation between applying the FTBPF to realvalued signals and forming the so called complex-valued analytic oscillations based on the Hilbert transform is indicated.

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