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This letter introduces a new approach for the demodulation of fringe patterns recorded in holographic interferometry using high-order ambiguity function (HAF). The proposed approach is capable of retrieving the phase from a single fringe pattern. The main advantage of this approach is that it directly provides an estimation of the continuous phase distribution and thereby avoids the necessity of using a cumbersome 2D phase unwrapping procedure. This method first computes the discrete-time analytic signal of the recorded fringe pattern. Then, by modelling this analytic signal as a polynomial phase signal embedded in additive complex white Gaussian noise, a parametric estimation procedure based on HAF is employed to directly estimate the unwrapped phase distribution. Numerical simulations and experimental results demonstrate the potential of the proposed approach.