The presented work addresses the issue of phase noise estimation for pilot-aided burst-mode transmission in digital communication systems. We propose to estimate the phase noise from a truncated discrete-cosine transform (DCT) expansion model. The key idea is to reconstruct the low-pass phase noise process via only a small number N of DCT coefficients of the phase expansion. An evident question that arises is how to choose N. Based on a few valid approximations, we derive an analytical expression of the bit-error rate (BER) degradation in the presence of residual phase noise, which allows us to determine the value of N that yields the minimum BER degradation.