A new method is proposed for the direct phase derivative estimation from a single spatial frequency modulated carrier fringe pattern in holographic interferometry. The fringe intensity in a given row/column is modeled as a difference equation of intensity with spatially varying coefficients. These coefficients carry the information on the phase derivative. Consequently, the accurate estimation of the coefficients is obtained by approximating the coefficients as a linear combination of the predefined linearly independent basis functions. Unlike Fourier transform based fringe analysis, the method does not call for performing the filtering of the Fourier spectrum of fringe intensity. Moreover, the estimation of the carrier frequency is performed by applying the proposed method to a reference interferogram. The performance of the proposed method is insensitive to the fringe amplitude modulation and is validated with the simulation results.