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An interpolation based digitizing method has been previously developed especially for the design of narrowband frequency selective filters. This method performs a trigonometric polynomial interpolation along an extended time window that ends at the current sampling time. The present paper reconsiders the basic extended window design (EWD) idea in the light of digital control systems requirements and proposes a generalized EWD (G-EWD) method. The main results of this paper are: (i) the closed-form G-EWD expressions derived for an interpolation space spanned by any set of linearly independent functions of time, (ii) a computationally efficient linear algebra generation of the G-EWD digital equivalents, and (iii) the derivation of optional prediction models whose output values are computed at fractional time instants beyond the current sampling time. Finally, the paper compares the proposed G-EWD method to an optimal frequency-domain digitizing method.