We present a channel spectral estimator for OFDM signals containing pilot carriers, assuming a known delay spread or a bound on this parameter. The estimator is based on modeling the channel's spectrum as a band-limited function, instead of as the discrete Fourier transform of a tapped delay line (TDL). Its main advantage is its immunity to the truncation mismatch in usual TDL models (Gibbs phenomenon). In order to assess the estimator, we compare it with the well-known TDL maximum likelihood (ML) estimator in terms of root-mean-square (RMS) error. The main result is that the proposed estimator improves on the ML estimator significantly, whenever the average spectral sampling rate is above the channel's delay spread. The improvement increases with the spectral oversampling ratio.