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Digital predistortion based on nonlinear system modeling and its inverse is an important technique for the linearization of radio frequency power amplifiers (PAs). Compensation for the nonlinear systems represented by polynomials involves polynomial inverses. In this paper, we propose a fast algorithm to invert a given baseband memoryless polynomial based on the predefined orthogonal basis. The orthogonal basis is predefined based on the distribution of the signal, which is known a priori. Compared with the well-established pth-order inverse method, the proposed algorithm can find the optimal coefficients of the inverse polynomial. Both numerical simulation and experiment with an actual PA demonstrate that the proposed algorithm can provide very good performance for compensating the nonlinear systems represented by baseband polynomial.