A new family of methods, named phase estimation using polyspectrum slices (PEP), for the reconstruction of the Fourier phase of a complex linear time invariant (LTI) system excited by a white non-Gaussian input is proposed. More precisely, we propose two subfamilies of methods, the q-PEP (q ges 3) and (q₁,q₂)-PEP (q₂ > q₁ ges 3) algorithms. The q-PEP methods exploit the best two-dimensional (2-D) slice of the data qth-order spectrum. The originality of the (q₁,q₂ )-PEP methods consists of exploiting simultaneously one 1-D slice of the q₁th-order spectrum and one 2-D slice of the q₂th-order spectrum. These new algorithms are easy both to implement and to use. Moreover, the asymptotic unbiasedness and consistency of these methods are demonstrated. Eventually, computer simulations show that the PEP algorithms exhibit in general better performances than classical methods especially for band-limited systems.