The presence of a frequency offset (FO) and phase noise can cause severe performance degradation in digital communication systems. This work combines a simple FO estimation technique with a low-complexity phase noise estimation method, inspired by the space-alternating generalized expectation-maximization algorithm. Using a truncated discrete-cosine transform (DCT) expansion, the phase noise estimate is derived from the estimated DCT coefficients of the phase. A number of implementations of the proposed algorithm are discussed. Numerical results indicate that when estimating the FO from pilot symbols only, comparable performance can be reached as the computationally more complex case where the FO is updated iteratively, with small convergence time. The phase noise estimation step is well capable of compensating for the residual FO. For the considered scenario, performing FO compensation before iterative phase noise estimation yields a bit-error rate performance degradation close to the case where the FO is known.