This paper proposes a tractable iterative scheme for computing parameter-dependent matrix sign function. It relies upon two results: (i) a fraction expansion of the matrix sign principal Padé rational approximation, (ii) a Discrete Fourier Transform (DFT) inversion method for polynomial parameter-dependent matrices. The method is used for solving parameter-dependent Riccati equations. Some illustrative examples, given throughout the paper, demonstrate the effectiveness of the method. An application for extracting the harmonics of current or voltage waveforms confirms the validity of the approach. A realistic control application dealing with a parameter dependent LQR design problem for an airfoil flutter is also presented.